Cálculo Exemplos

$f (x) = {(3 x^{3} + 7)}^{7}$

Etapa 1

Encontre a primeira derivada.

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Etapa 1.1

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{7}$ e $g (x) = 3 x^{3} + 7$ .

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Etapa 1.1.1

Para aplicar a regra da cadeia, defina $u$ como $3 x^{3} + 7$ .

$f' (x) = \frac{d}{d u} (u^{7}) \frac{d}{d x} (3 x^{3} + 7)$

Etapa 1.1.2

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d u} [u^{n}]$ é $n u^{n - 1}$ , em que $n = 7$ .

$f' (x) = 7 u^{6} \frac{d}{d x} (3 x^{3} + 7)$

Etapa 1.1.3

Substitua todas as ocorrências de $u$ por $3 x^{3} + 7$ .

$f' (x) = 7 {(3 x^{3} + 7)}^{6} \frac{d}{d x} (3 x^{3} + 7)$

Etapa 1.2

Diferencie.

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Etapa 1.2.1

De acordo com a regra da soma, a derivada de $3 x^{3} + 7$ com relação a $x$ é $\frac{d}{d x} [3 x^{3}] + \frac{d}{d x} [7]$ .

$f' (x) = 7 {(3 x^{3} + 7)}^{6} (\frac{d}{d x} (3 x^{3}) + \frac{d}{d x} (7))$

Etapa 1.2.2

Como $3$ é constante em relação a $x$ , a derivada de $3 x^{3}$ em relação a $x$ é $3 \frac{d}{d x} [x^{3}]$ .

$f' (x) = 7 {(3 x^{3} + 7)}^{6} (3 \frac{d}{d x} (x^{3}) + \frac{d}{d x} (7))$

Etapa 1.2.3

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

$f' (x) = 7 {(3 x^{3} + 7)}^{6} (3 (3 x^{2}) + \frac{d}{d x} (7))$

Etapa 1.2.4

Multiplique $3$ por $3$ .

$f' (x) = 7 {(3 x^{3} + 7)}^{6} (9 x^{2} + \frac{d}{d x} (7))$

Etapa 1.2.5

Como $7$ é constante em relação a $x$ , a derivada de $7$ em relação a $x$ é $0$ .

$f' (x) = 7 {(3 x^{3} + 7)}^{6} (9 x^{2} + 0)$

Etapa 1.2.6

Simplifique a expressão.

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Etapa 1.2.6.1

Some $9 x^{2}$ e $0$ .

$f' (x) = 7 {(3 x^{3} + 7)}^{6} (9 x^{2})$

Etapa 1.2.6.2

Multiplique $9$ por $7$ .

$f' (x) = 63 {(3 x^{3} + 7)}^{6} x^{2}$

Etapa 1.2.6.3

Reordene os fatores de $63 {(3 x^{3} + 7)}^{6} x^{2}$ .

$f' (x) = 63 x^{2} {(3 x^{3} + 7)}^{6}$

Etapa 2

Encontre a segunda derivada.

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Etapa 2.1

Como $63$ é constante em relação a $x$ , a derivada de $63 x^{2} {(3 x^{3} + 7)}^{6}$ em relação a $x$ é $63 \frac{d}{d x} [x^{2} {(3 x^{3} + 7)}^{6}]$ .

$f'' (x) = 63 \frac{d}{d x} (x^{2} {(3 x^{3} + 7)}^{6})$

Etapa 2.2

Diferencie usando a regra do produto, que determina que $\frac{d}{d x} [f (x) g (x)]$ é $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ , em que $f (x) = x^{2}$ e $g (x) = {(3 x^{3} + 7)}^{6}$ .

$f'' (x) = 63 (x^{2} \frac{d}{d x} ({(3 x^{3} + 7)}^{6}) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.3

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{6}$ e $g (x) = 3 x^{3} + 7$ .

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Etapa 2.3.1

Para aplicar a regra da cadeia, defina $u$ como $3 x^{3} + 7$ .

$f'' (x) = 63 (x^{2} (\frac{d}{d u} (u^{6}) \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.3.2

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d u} [u^{n}]$ é $n u^{n - 1}$ , em que $n = 6$ .

$f'' (x) = 63 (x^{2} (6 u^{5} \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.3.3

Substitua todas as ocorrências de $u$ por $3 x^{3} + 7$ .

$f'' (x) = 63 (x^{2} (6 {(3 x^{3} + 7)}^{5} \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.4

Diferencie.

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Etapa 2.4.1

De acordo com a regra da soma, a derivada de $3 x^{3} + 7$ com relação a $x$ é $\frac{d}{d x} [3 x^{3}] + \frac{d}{d x} [7]$ .

$f'' (x) = 63 (x^{2} (6 {(3 x^{3} + 7)}^{5} (\frac{d}{d x} (3 x^{3}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.4.2

Como $3$ é constante em relação a $x$ , a derivada de $3 x^{3}$ em relação a $x$ é $3 \frac{d}{d x} [x^{3}]$ .

$f'' (x) = 63 (x^{2} (6 {(3 x^{3} + 7)}^{5} (3 \frac{d}{d x} (x^{3}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.4.3

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

$f'' (x) = 63 (x^{2} (6 {(3 x^{3} + 7)}^{5} (3 (3 x^{2}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.4.4

Multiplique $3$ por $3$ .

$f'' (x) = 63 (x^{2} (6 {(3 x^{3} + 7)}^{5} (9 x^{2} + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.4.5

Como $7$ é constante em relação a $x$ , a derivada de $7$ em relação a $x$ é $0$ .

$f'' (x) = 63 (x^{2} (6 {(3 x^{3} + 7)}^{5} (9 x^{2} + 0)) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.4.6

Simplifique a expressão.

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Etapa 2.4.6.1

Some $9 x^{2}$ e $0$ .

$f'' (x) = 63 (x^{2} (6 {(3 x^{3} + 7)}^{5} (9 x^{2})) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.4.6.2

Multiplique $9$ por $6$ .

$f'' (x) = 63 (x^{2} (54 {(3 x^{3} + 7)}^{5} x^{2}) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.5

Multiplique $x^{2}$ por $x^{2}$ somando os expoentes.

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Etapa 2.5.1

Mova $x^{2}$ .

$f'' (x) = 63 (x^{2} x^{2} (54 {(3 x^{3} + 7)}^{5}) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.5.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f'' (x) = 63 (x^{2 + 2} (54 {(3 x^{3} + 7)}^{5}) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.5.3

Some $2$ e $2$ .

$f'' (x) = 63 (x^{4} (54 {(3 x^{3} + 7)}^{5}) + {(3 x^{3} + 7)}^{6} \frac{d}{d x} (x^{2}))$

Etapa 2.6

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 2$ .

$f'' (x) = 63 (x^{4} (54 {(3 x^{3} + 7)}^{5}) + {(3 x^{3} + 7)}^{6} (2 x))$

Etapa 2.7

Mova $2$ para a esquerda de ${(3 x^{3} + 7)}^{6}$ .

$f'' (x) = 63 (x^{4} (54 {(3 x^{3} + 7)}^{5}) + 2 \cdot ({(3 x^{3} + 7)}^{6} x))$

Etapa 2.8

Simplifique.

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Etapa 2.8.1

Aplique a propriedade distributiva.

$f'' (x) = 63 (x^{4} (54 {(3 x^{3} + 7)}^{5})) + 63 (2 {(3 x^{3} + 7)}^{6} x)$

Etapa 2.8.2

Multiplique $54$ por $63$ .

$f'' (x) = 3402 (x^{4} ({(3 x^{3} + 7)}^{5})) + 63 (2 {(3 x^{3} + 7)}^{6} x)$

Etapa 2.8.3

Multiplique $2$ por $63$ .

$f'' (x) = 3402 x^{4} {(3 x^{3} + 7)}^{5} + 126 ({(3 x^{3} + 7)}^{6} x)$

Etapa 2.8.4

Fatore $126 x {(3 x^{3} + 7)}^{5}$ de $3402 x^{4} {(3 x^{3} + 7)}^{5} + 126 {(3 x^{3} + 7)}^{6} x$ .

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Etapa 2.8.4.1

Fatore $126 x {(3 x^{3} + 7)}^{5}$ de $3402 x^{4} {(3 x^{3} + 7)}^{5}$ .

$f'' (x) = 126 x {(3 x^{3} + 7)}^{5} (27 x^{3}) + 126 {(3 x^{3} + 7)}^{6} x$

Etapa 2.8.4.2

Fatore $126 x {(3 x^{3} + 7)}^{5}$ de $126 {(3 x^{3} + 7)}^{6} x$ .

$f'' (x) = 126 x {(3 x^{3} + 7)}^{5} (27 x^{3}) + 126 x {(3 x^{3} + 7)}^{5} (3 x^{3} + 7)$

Etapa 2.8.4.3

Fatore $126 x {(3 x^{3} + 7)}^{5}$ de $126 x {(3 x^{3} + 7)}^{5} (27 x^{3}) + 126 x {(3 x^{3} + 7)}^{5} (3 x^{3} + 7)$ .

$f'' (x) = 126 x {(3 x^{3} + 7)}^{5} (27 x^{3} + 3 x^{3} + 7)$

Etapa 2.8.5

Some $27 x^{3}$ e $3 x^{3}$ .

$f'' (x) = 126 x {(3 x^{3} + 7)}^{5} (30 x^{3} + 7)$

Etapa 3

Encontre a terceira derivada.

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Etapa 3.1

Como $126$ é constante em relação a $x$ , a derivada de $126 x {(3 x^{3} + 7)}^{5} (30 x^{3} + 7)$ em relação a $x$ é $126 \frac{d}{d x} [x {(3 x^{3} + 7)}^{5} (30 x^{3} + 7)]$ .

$f''' (x) = 126 \frac{d}{d x} (x {(3 x^{3} + 7)}^{5} (30 x^{3} + 7))$

Etapa 3.2

Diferencie usando a regra do produto, que determina que $\frac{d}{d x} [f (x) g (x)]$ é $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ , em que $f (x) = x {(3 x^{3} + 7)}^{5}$ e $g (x) = 30 x^{3} + 7$ .

$f''' (x) = 126 (x {(3 x^{3} + 7)}^{5} \frac{d}{d x} (30 x^{3} + 7) + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.3

Diferencie.

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Etapa 3.3.1

De acordo com a regra da soma, a derivada de $30 x^{3} + 7$ com relação a $x$ é $\frac{d}{d x} [30 x^{3}] + \frac{d}{d x} [7]$ .

$f''' (x) = 126 (x {(3 x^{3} + 7)}^{5} (\frac{d}{d x} (30 x^{3}) + \frac{d}{d x} (7)) + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.3.2

Como $30$ é constante em relação a $x$ , a derivada de $30 x^{3}$ em relação a $x$ é $30 \frac{d}{d x} [x^{3}]$ .

$f''' (x) = 126 (x {(3 x^{3} + 7)}^{5} (30 \frac{d}{d x} (x^{3}) + \frac{d}{d x} (7)) + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.3.3

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

$f''' (x) = 126 (x {(3 x^{3} + 7)}^{5} (30 (3 x^{2}) + \frac{d}{d x} (7)) + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.3.4

Multiplique $3$ por $30$ .

$f''' (x) = 126 (x {(3 x^{3} + 7)}^{5} (90 x^{2} + \frac{d}{d x} (7)) + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.3.5

Como $7$ é constante em relação a $x$ , a derivada de $7$ em relação a $x$ é $0$ .

$f''' (x) = 126 (x {(3 x^{3} + 7)}^{5} (90 x^{2} + 0) + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.3.6

Some $90 x^{2}$ e $0$ .

$f''' (x) = 126 (x {(3 x^{3} + 7)}^{5} (90 x^{2}) + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.4

Eleve $x$ à potência de $1$ .

$f''' (x) = 126 (x^{2} x {(3 x^{3} + 7)}^{5} \cdot 90 + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.5

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f''' (x) = 126 (x^{2 + 1} {(3 x^{3} + 7)}^{5} \cdot 90 + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.6

Simplifique a expressão.

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Etapa 3.6.1

Some $2$ e $1$ .

$f''' (x) = 126 (x^{3} {(3 x^{3} + 7)}^{5} \cdot 90 + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.6.2

Mova $90$ para a esquerda de $x^{3} {(3 x^{3} + 7)}^{5}$ .

$f''' (x) = 126 (90 \cdot (x^{3} {(3 x^{3} + 7)}^{5}) + (30 x^{3} + 7) \frac{d}{d x} (x {(3 x^{3} + 7)}^{5}))$

Etapa 3.7

Diferencie usando a regra do produto, que determina que $\frac{d}{d x} [f (x) g (x)]$ é $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ , em que $f (x) = x$ e $g (x) = {(3 x^{3} + 7)}^{5}$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x \frac{d}{d x} ({(3 x^{3} + 7)}^{5}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.8

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{5}$ e $g (x) = 3 x^{3} + 7$ .

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Etapa 3.8.1

Para aplicar a regra da cadeia, defina $u$ como $3 x^{3} + 7$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (\frac{d}{d u} (u^{5}) \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.8.2

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d u} [u^{n}]$ é $n u^{n - 1}$ , em que $n = 5$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (5 u^{4} \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.8.3

Substitua todas as ocorrências de $u$ por $3 x^{3} + 7$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (5 {(3 x^{3} + 7)}^{4} \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.9

Diferencie.

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Etapa 3.9.1

De acordo com a regra da soma, a derivada de $3 x^{3} + 7$ com relação a $x$ é $\frac{d}{d x} [3 x^{3}] + \frac{d}{d x} [7]$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (5 {(3 x^{3} + 7)}^{4} (\frac{d}{d x} (3 x^{3}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.9.2

Como $3$ é constante em relação a $x$ , a derivada de $3 x^{3}$ em relação a $x$ é $3 \frac{d}{d x} [x^{3}]$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (5 {(3 x^{3} + 7)}^{4} (3 \frac{d}{d x} (x^{3}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.9.3

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (5 {(3 x^{3} + 7)}^{4} (3 (3 x^{2}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.9.4

Multiplique $3$ por $3$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (5 {(3 x^{3} + 7)}^{4} (9 x^{2} + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.9.5

Como $7$ é constante em relação a $x$ , a derivada de $7$ em relação a $x$ é $0$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (5 {(3 x^{3} + 7)}^{4} (9 x^{2} + 0)) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.9.6

Simplifique a expressão.

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Etapa 3.9.6.1

Some $9 x^{2}$ e $0$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (5 {(3 x^{3} + 7)}^{4} (9 x^{2})) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.9.6.2

Multiplique $9$ por $5$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x (45 {(3 x^{3} + 7)}^{4} x^{2}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.10

Eleve $x$ à potência de $1$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x^{2} x (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.11

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x^{2 + 1} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.12

Some $2$ e $1$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x)))$

Etapa 3.13

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 1$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5} \cdot 1))$

Etapa 3.14

Multiplique ${(3 x^{3} + 7)}^{5}$ por $1$ .

$f''' (x) = 126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}))$

Etapa 4

Encontre a quarta derivada.

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Etapa 4.1

Diferencie.

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Etapa 4.1.1

Como $126$ é constante em relação a $x$ , a derivada de $126 (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}))$ em relação a $x$ é $126 \frac{d}{d x} [90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})]$ .

$f^{4} (x) = 126 \frac{d}{d x} (90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}))$

Etapa 4.1.2

De acordo com a regra da soma, a derivada de $90 x^{3} {(3 x^{3} + 7)}^{5} + (30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})$ com relação a $x$ é $\frac{d}{d x} [90 x^{3} {(3 x^{3} + 7)}^{5}] + \frac{d}{d x} [(30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})]$ .

$f^{4} (x) = 126 (\frac{d}{d x} (90 x^{3} {(3 x^{3} + 7)}^{5}) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.1.3

Como $90$ é constante em relação a $x$ , a derivada de $90 x^{3} {(3 x^{3} + 7)}^{5}$ em relação a $x$ é $90 \frac{d}{d x} [x^{3} {(3 x^{3} + 7)}^{5}]$ .

$f^{4} (x) = 126 (90 \frac{d}{d x} (x^{3} {(3 x^{3} + 7)}^{5}) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.2

Diferencie usando a regra do produto, que determina que $\frac{d}{d x} [f (x) g (x)]$ é $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ , em que $f (x) = x^{3}$ e $g (x) = {(3 x^{3} + 7)}^{5}$ .

$f^{4} (x) = 126 (90 (x^{3} \frac{d}{d x} ({(3 x^{3} + 7)}^{5}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.3

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{5}$ e $g (x) = 3 x^{3} + 7$ .

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Etapa 4.3.1

Para aplicar a regra da cadeia, defina $u_{1}$ como $3 x^{3} + 7$ .

$f^{4} (x) = 126 (90 (x^{3} (\frac{d}{d u (1)} ({u_{1}}^{5}) \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.3.2

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d u_{1}} [{u_{1}}^{n}]$ é $n {u_{1}}^{n - 1}$ , em que $n = 5$ .

$f^{4} (x) = 126 (90 (x^{3} (5 {u_{1}}^{4} \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.3.3

Substitua todas as ocorrências de $u_{1}$ por $3 x^{3} + 7$ .

$f^{4} (x) = 126 (90 (x^{3} (5 {(3 x^{3} + 7)}^{4} \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.4

Diferencie.

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Etapa 4.4.1

De acordo com a regra da soma, a derivada de $3 x^{3} + 7$ com relação a $x$ é $\frac{d}{d x} [3 x^{3}] + \frac{d}{d x} [7]$ .

$f^{4} (x) = 126 (90 (x^{3} (5 {(3 x^{3} + 7)}^{4} (\frac{d}{d x} (3 x^{3}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.4.2

Como $3$ é constante em relação a $x$ , a derivada de $3 x^{3}$ em relação a $x$ é $3 \frac{d}{d x} [x^{3}]$ .

$f^{4} (x) = 126 (90 (x^{3} (5 {(3 x^{3} + 7)}^{4} (3 \frac{d}{d x} (x^{3}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.4.3

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

$f^{4} (x) = 126 (90 (x^{3} (5 {(3 x^{3} + 7)}^{4} (3 (3 x^{2}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.4.4

Multiplique $3$ por $3$ .

$f^{4} (x) = 126 (90 (x^{3} (5 {(3 x^{3} + 7)}^{4} (9 x^{2} + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.4.5

Como $7$ é constante em relação a $x$ , a derivada de $7$ em relação a $x$ é $0$ .

$f^{4} (x) = 126 (90 (x^{3} (5 {(3 x^{3} + 7)}^{4} (9 x^{2} + 0)) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.4.6

Simplifique a expressão.

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Etapa 4.4.6.1

Some $9 x^{2}$ e $0$ .

$f^{4} (x) = 126 (90 (x^{3} (5 {(3 x^{3} + 7)}^{4} (9 x^{2})) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.4.6.2

Multiplique $9$ por $5$ .

$f^{4} (x) = 126 (90 (x^{3} (45 {(3 x^{3} + 7)}^{4} x^{2}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.5

Multiplique $x^{3}$ por $x^{2}$ somando os expoentes.

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Etapa 4.5.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (90 (x^{2} x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.5.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (90 (x^{2 + 3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.5.3

Some $2$ e $3$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.6

Diferencie usando a regra da multiplicação de potências.

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Etapa 4.6.1

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5} (3 x^{2})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.6.2

Mova $3$ para a esquerda de ${(3 x^{3} + 7)}^{5}$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 \cdot ({(3 x^{3} + 7)}^{5} x^{2})) + \frac{d}{d x} ((30 x^{3} + 7) (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5})))$

Etapa 4.7

Diferencie usando a regra do produto, que determina que $\frac{d}{d x} [f (x) g (x)]$ é $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ , em que $f (x) = 30 x^{3} + 7$ e $g (x) = x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) \frac{d}{d x} (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.8

Diferencie.

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Etapa 4.8.1

De acordo com a regra da soma, a derivada de $x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}$ com relação a $x$ é $\frac{d}{d x} [x^{3} (45 {(3 x^{3} + 7)}^{4})] + \frac{d}{d x} [{(3 x^{3} + 7)}^{5}]$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (\frac{d}{d x} (x^{3} (45 {(3 x^{3} + 7)}^{4})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.8.2

Como $45$ é constante em relação a $x$ , a derivada de $x^{3} (45 {(3 x^{3} + 7)}^{4})$ em relação a $x$ é $45 \frac{d}{d x} [x^{3} ({(3 x^{3} + 7)}^{4})]$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 \frac{d}{d x} (x^{3} ({(3 x^{3} + 7)}^{4})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.9

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} \frac{d}{d x} ({(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.10

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{4}$ e $g (x) = 3 x^{3} + 7$ .

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Etapa 4.10.1

Para aplicar a regra da cadeia, defina $u_{2}$ como $3 x^{3} + 7$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (\frac{d}{d u (2)} ({u_{2}}^{4}) \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.10.2

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d u_{2}} [{u_{2}}^{n}]$ é $n {u_{2}}^{n - 1}$ , em que $n = 4$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (4 {u_{2}}^{3} \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.10.3

Substitua todas as ocorrências de $u_{2}$ por $3 x^{3} + 7$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (4 {(3 x^{3} + 7)}^{3} \frac{d}{d x} (3 x^{3} + 7)) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.11

Diferencie.

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Etapa 4.11.1

De acordo com a regra da soma, a derivada de $3 x^{3} + 7$ com relação a $x$ é $\frac{d}{d x} [3 x^{3}] + \frac{d}{d x} [7]$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (4 {(3 x^{3} + 7)}^{3} (\frac{d}{d x} (3 x^{3}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.11.2

Como $3$ é constante em relação a $x$ , a derivada de $3 x^{3}$ em relação a $x$ é $3 \frac{d}{d x} [x^{3}]$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (4 {(3 x^{3} + 7)}^{3} (3 \frac{d}{d x} (x^{3}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.11.3

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (4 {(3 x^{3} + 7)}^{3} (3 (3 x^{2}) + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.11.4

Multiplique $3$ por $3$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (4 {(3 x^{3} + 7)}^{3} (9 x^{2} + \frac{d}{d x} (7))) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.11.5

Como $7$ é constante em relação a $x$ , a derivada de $7$ em relação a $x$ é $0$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (4 {(3 x^{3} + 7)}^{3} (9 x^{2} + 0)) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.11.6

Simplifique a expressão.

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Etapa 4.11.6.1

Some $9 x^{2}$ e $0$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (4 {(3 x^{3} + 7)}^{3} (9 x^{2})) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.11.6.2

Multiplique $9$ por $4$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{3} (36 {(3 x^{3} + 7)}^{3} x^{2}) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.12

Multiplique $x^{3}$ por $x^{2}$ somando os expoentes.

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Etapa 4.12.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{2} x^{3} (36 {(3 x^{3} + 7)}^{3}) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.12.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{2 + 3} (36 {(3 x^{3} + 7)}^{3}) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.12.3

Some $2$ e $3$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + {(3 x^{3} + 7)}^{4} \frac{d}{d x} (x^{3})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.13

Diferencie usando a regra da multiplicação de potências.

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Etapa 4.13.1

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + {(3 x^{3} + 7)}^{4} (3 x^{2})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.13.2

Mova $3$ para a esquerda de ${(3 x^{3} + 7)}^{4}$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 \cdot ({(3 x^{3} + 7)}^{4} x^{2})) + \frac{d}{d x} ({(3 x^{3} + 7)}^{5})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.14

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{5}$ e $g (x) = 3 x^{3} + 7$ .

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Etapa 4.14.1

Para aplicar a regra da cadeia, defina $u_{3}$ como $3 x^{3} + 7$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + \frac{d}{d u (3)} ({u_{3}}^{5}) \frac{d}{d x} (3 x^{3} + 7)) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.14.2

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d u_{3}} [{u_{3}}^{n}]$ é $n {u_{3}}^{n - 1}$ , em que $n = 5$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 5 {u_{3}}^{4} \frac{d}{d x} (3 x^{3} + 7)) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.14.3

Substitua todas as ocorrências de $u_{3}$ por $3 x^{3} + 7$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 5 {(3 x^{3} + 7)}^{4} \frac{d}{d x} (3 x^{3} + 7)) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.15

Diferencie.

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Etapa 4.15.1

De acordo com a regra da soma, a derivada de $3 x^{3} + 7$ com relação a $x$ é $\frac{d}{d x} [3 x^{3}] + \frac{d}{d x} [7]$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 5 {(3 x^{3} + 7)}^{4} (\frac{d}{d x} (3 x^{3}) + \frac{d}{d x} (7))) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.15.2

Como $3$ é constante em relação a $x$ , a derivada de $3 x^{3}$ em relação a $x$ é $3 \frac{d}{d x} [x^{3}]$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 5 {(3 x^{3} + 7)}^{4} (3 \frac{d}{d x} (x^{3}) + \frac{d}{d x} (7))) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.15.3

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 5 {(3 x^{3} + 7)}^{4} (3 (3 x^{2}) + \frac{d}{d x} (7))) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.15.4

Multiplique $3$ por $3$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 5 {(3 x^{3} + 7)}^{4} (9 x^{2} + \frac{d}{d x} (7))) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.15.5

Como $7$ é constante em relação a $x$ , a derivada de $7$ em relação a $x$ é $0$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 5 {(3 x^{3} + 7)}^{4} (9 x^{2} + 0)) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.15.6

Simplifique a expressão.

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Etapa 4.15.6.1

Some $9 x^{2}$ e $0$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 5 {(3 x^{3} + 7)}^{4} (9 x^{2})) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.15.6.2

Multiplique $9$ por $5$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2}) + (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) \frac{d}{d x} (30 x^{3} + 7))$

Etapa 4.15.7

De acordo com a regra da soma, a derivada de $30 x^{3} + 7$ com relação a $x$ é $\frac{d}{d x} [30 x^{3}] + \frac{d}{d x} [7]$ .

Etapa 4.15.8

Como $30$ é constante em relação a $x$ , a derivada de $30 x^{3}$ em relação a $x$ é $30 \frac{d}{d x} [x^{3}]$ .

Etapa 4.15.9

Diferencie usando a regra da multiplicação de potências, que determina que $\frac{d}{d x} [x^{n}]$ é $n x^{n - 1}$ , em que $n = 3$ .

Etapa 4.15.10

Multiplique $3$ por $30$ .

Etapa 4.15.11

Como $7$ é constante em relação a $x$ , a derivada de $7$ em relação a $x$ é $0$ .

Etapa 4.15.12

Simplifique a expressão.

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Etapa 4.15.12.1

Some $90 x^{2}$ e $0$ .

Etapa 4.15.12.2

Mova $90$ para a esquerda de $x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}$ .

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}) + 3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2}) + 90 \cdot ((x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) x^{2}))$

Etapa 4.16

Simplifique.

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Etapa 4.16.1

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4})) + 90 (3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3}) + 3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2}) + 90 (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) x^{2})$

Etapa 4.16.2

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4})) + 90 (3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3})) + 45 (3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2}) + 90 (x^{3} (45 {(3 x^{3} + 7)}^{4}) + {(3 x^{3} + 7)}^{5}) x^{2})$

Etapa 4.16.3

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4})) + 90 (3 {(3 x^{3} + 7)}^{5} x^{2}) + (30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3})) + 45 (3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2}) + (90 (x^{3} (45 {(3 x^{3} + 7)}^{4})) + 90 {(3 x^{3} + 7)}^{5}) x^{2})$

Etapa 4.16.4

Aplique a propriedade distributiva.

Etapa 4.16.5

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (90 (x^{5} (45 {(3 x^{3} + 7)}^{4}))) + 126 (90 (3 {(3 x^{3} + 7)}^{5} x^{2})) + 126 ((30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3})) + 45 (3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2})) + 126 (90 (x^{3} (45 {(3 x^{3} + 7)}^{4})) x^{2}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.6

Multiplique $45$ por $90$ .

$f^{4} (x) = 126 (4050 (x^{5} ({(3 x^{3} + 7)}^{4}))) + 126 (90 (3 {(3 x^{3} + 7)}^{5} x^{2})) + 126 ((30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3})) + 45 (3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2})) + 126 (90 (x^{3} (45 {(3 x^{3} + 7)}^{4})) x^{2}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.7

Multiplique $4050$ por $126$ .

$f^{4} (x) = 510300 (x^{5} {(3 x^{3} + 7)}^{4}) + 126 (90 (3 {(3 x^{3} + 7)}^{5} x^{2})) + 126 ((30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3})) + 45 (3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2})) + 126 (90 (x^{3} (45 {(3 x^{3} + 7)}^{4})) x^{2}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.8

Multiplique $3$ por $90$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 126 (270 ({(3 x^{3} + 7)}^{5} x^{2})) + 126 ((30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3})) + 45 (3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2})) + 126 (90 (x^{3} (45 {(3 x^{3} + 7)}^{4})) x^{2}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.9

Multiplique $270$ por $126$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 ({(3 x^{3} + 7)}^{5} x^{2}) + 126 ((30 x^{3} + 7) (45 (x^{5} (36 {(3 x^{3} + 7)}^{3})) + 45 (3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2})) + 126 (90 (x^{3} (45 {(3 x^{3} + 7)}^{4})) x^{2}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.10

Multiplique $36$ por $45$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 ((30 x^{3} + 7) (1620 (x^{5} ({(3 x^{3} + 7)}^{3})) + 45 (3 {(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2})) + 126 (90 (x^{3} (45 {(3 x^{3} + 7)}^{4})) x^{2}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.11

Multiplique $3$ por $45$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 ((30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 135 ({(3 x^{3} + 7)}^{4} x^{2}) + 45 {(3 x^{3} + 7)}^{4} x^{2})) + 126 (90 (x^{3} (45 {(3 x^{3} + 7)}^{4})) x^{2}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.12

Some $135 {(3 x^{3} + 7)}^{4} x^{2}$ e $45 {(3 x^{3} + 7)}^{4} x^{2}$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 ((30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2})) + 126 (90 (x^{3} (45 {(3 x^{3} + 7)}^{4})) x^{2}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.13

Multiplique $45$ por $90$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}) + 126 (4050 (x^{3} ({(3 x^{3} + 7)}^{4})) x^{2}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.14

Multiplique $x^{3}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.14.1

Mova $x^{2}$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}) + 126 (4050 (x^{2} x^{3}) {(3 x^{3} + 7)}^{4}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.14.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}) + 126 (4050 x^{2 + 3} {(3 x^{3} + 7)}^{4}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.14.3

Some $2$ e $3$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}) + 126 (4050 x^{5} {(3 x^{3} + 7)}^{4}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.15

Multiplique $4050$ por $126$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}) + 510300 (x^{5} {(3 x^{3} + 7)}^{4}) + 126 (90 {(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.16

Multiplique $90$ por $126$ .

$f^{4} (x) = 510300 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}) + 510300 x^{5} {(3 x^{3} + 7)}^{4} + 11340 ({(3 x^{3} + 7)}^{5} x^{2})$

Etapa 4.16.17

Some $510300 x^{5} {(3 x^{3} + 7)}^{4}$ e $510300 x^{5} {(3 x^{3} + 7)}^{4}$ .

$f^{4} (x) = 1020600 x^{5} {(3 x^{3} + 7)}^{4} + 34020 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}) + 11340 {(3 x^{3} + 7)}^{5} x^{2}$

Etapa 4.16.18

Some $34020 {(3 x^{3} + 7)}^{5} x^{2}$ e $11340 {(3 x^{3} + 7)}^{5} x^{2}$ .

$f^{4} (x) = 1020600 x^{5} {(3 x^{3} + 7)}^{4} + 45360 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2})$

Etapa 4.16.19

Fatore $126$ de $1020600 x^{5} {(3 x^{3} + 7)}^{4} + 45360 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2})$ .

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Etapa 4.16.19.1

Fatore $126$ de $1020600 x^{5} {(3 x^{3} + 7)}^{4}$ .

$f^{4} (x) = 126 (8100 x^{5} {(3 x^{3} + 7)}^{4}) + 45360 {(3 x^{3} + 7)}^{5} x^{2} + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2})$

Etapa 4.16.19.2

Fatore $126$ de $45360 {(3 x^{3} + 7)}^{5} x^{2}$ .

$f^{4} (x) = 126 (8100 x^{5} {(3 x^{3} + 7)}^{4}) + 126 (360 {(3 x^{3} + 7)}^{5} x^{2}) + 126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2})$

Etapa 4.16.19.3

Fatore $126$ de $126 (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2})$ .

$f^{4} (x) = 126 (8100 x^{5} {(3 x^{3} + 7)}^{4}) + 126 (360 {(3 x^{3} + 7)}^{5} x^{2}) + 126 ((30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.19.4

Fatore $126$ de $126 (8100 x^{5} {(3 x^{3} + 7)}^{4}) + 126 (360 {(3 x^{3} + 7)}^{5} x^{2})$ .

$f^{4} (x) = 126 (8100 x^{5} {(3 x^{3} + 7)}^{4} + 360 {(3 x^{3} + 7)}^{5} x^{2}) + 126 ((30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.19.5

Fatore $126$ de $126 (8100 x^{5} {(3 x^{3} + 7)}^{4} + 360 {(3 x^{3} + 7)}^{5} x^{2}) + 126 ((30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$ .

$f^{4} (x) = 126 (8100 x^{5} {(3 x^{3} + 7)}^{4} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20

Simplifique cada termo.

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Etapa 4.16.20.1

Use o teorema binomial.

$f^{4} (x) = 126 (8100 x^{5} ({(3 x^{3})}^{4} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2

Simplifique cada termo.

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Etapa 4.16.20.2.1

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (8100 x^{5} (3^{4} {(x^{3})}^{4} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.2

Eleve $3$ à potência de $4$ .

$f^{4} (x) = 126 (8100 x^{5} (81 {(x^{3})}^{4} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.3

Multiplique os expoentes em ${(x^{3})}^{4}$ .

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Etapa 4.16.20.2.3.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{3 \cdot 4} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.3.2

Multiplique $3$ por $4$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.4

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 4 (3^{3} {(x^{3})}^{3}) \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.5

Eleve $3$ à potência de $3$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 4 (27 {(x^{3})}^{3}) \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.6

Multiplique os expoentes em ${(x^{3})}^{3}$ .

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Etapa 4.16.20.2.6.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 4 (27 x^{3 \cdot 3}) \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.6.2

Multiplique $3$ por $3$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 4 (27 x^{9}) \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.7

Multiplique $27$ por $4$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 108 x^{9} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.8

Multiplique $7$ por $108$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.9

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 6 (3^{2} {(x^{3})}^{2}) \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.10

Eleve $3$ à potência de $2$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 6 (9 {(x^{3})}^{2}) \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.11

Multiplique os expoentes em ${(x^{3})}^{2}$ .

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Etapa 4.16.20.2.11.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 6 (9 x^{3 \cdot 2}) \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.11.2

Multiplique $3$ por $2$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 6 (9 x^{6}) \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.12

Multiplique $9$ por $6$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 54 x^{6} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.13

Eleve $7$ à potência de $2$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 54 x^{6} \cdot 49 + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.14

Multiplique $49$ por $54$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 2646 x^{6} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.15

Multiplique $3$ por $4$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 2646 x^{6} + 12 x^{3} \cdot 7^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.16

Eleve $7$ à potência de $3$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 2646 x^{6} + 12 x^{3} \cdot 343 + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.17

Multiplique $343$ por $12$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 2646 x^{6} + 4116 x^{3} + 7^{4}) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.2.18

Eleve $7$ à potência de $4$ .

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12} + 756 x^{9} + 2646 x^{6} + 4116 x^{3} + 2401) + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.3

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (8100 x^{5} (81 x^{12}) + 8100 x^{5} (756 x^{9}) + 8100 x^{5} (2646 x^{6}) + 8100 x^{5} (4116 x^{3}) + 8100 x^{5} \cdot 2401 + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.4

Simplifique.

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Etapa 4.16.20.4.1

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (8100 \cdot (81 x^{5} x^{12}) + 8100 x^{5} (756 x^{9}) + 8100 x^{5} (2646 x^{6}) + 8100 x^{5} (4116 x^{3}) + 8100 x^{5} \cdot 2401 + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.4.2

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (8100 \cdot (81 x^{5} x^{12}) + 8100 \cdot (756 x^{5} x^{9}) + 8100 x^{5} (2646 x^{6}) + 8100 x^{5} (4116 x^{3}) + 8100 x^{5} \cdot 2401 + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.4.3

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (8100 \cdot (81 x^{5} x^{12}) + 8100 \cdot (756 x^{5} x^{9}) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 x^{5} (4116 x^{3}) + 8100 x^{5} \cdot 2401 + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.4.4

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (8100 \cdot (81 x^{5} x^{12}) + 8100 \cdot (756 x^{5} x^{9}) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 8100 x^{5} \cdot 2401 + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.4.5

Multiplique $2401$ por $8100$ .

$f^{4} (x) = 126 (8100 \cdot (81 x^{5} x^{12}) + 8100 \cdot (756 x^{5} x^{9}) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5

Simplifique cada termo.

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Etapa 4.16.20.5.1

Multiplique $x^{5}$ por $x^{12}$ somando os expoentes.

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Etapa 4.16.20.5.1.1

Mova $x^{12}$ .

$f^{4} (x) = 126 (8100 \cdot (81 (x^{12} x^{5})) + 8100 \cdot (756 x^{5} x^{9}) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.1.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (8100 \cdot (81 x^{12 + 5}) + 8100 \cdot (756 x^{5} x^{9}) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.1.3

Some $12$ e $5$ .

$f^{4} (x) = 126 (8100 \cdot (81 x^{17}) + 8100 \cdot (756 x^{5} x^{9}) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.2

Multiplique $8100$ por $81$ .

$f^{4} (x) = 126 (656100 x^{17} + 8100 \cdot (756 x^{5} x^{9}) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.3

Multiplique $x^{5}$ por $x^{9}$ somando os expoentes.

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Etapa 4.16.20.5.3.1

Mova $x^{9}$ .

$f^{4} (x) = 126 (656100 x^{17} + 8100 \cdot (756 (x^{9} x^{5})) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.3.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 8100 \cdot (756 x^{9 + 5}) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.3.3

Some $9$ e $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 8100 \cdot (756 x^{14}) + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.4

Multiplique $8100$ por $756$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 8100 \cdot (2646 x^{5} x^{6}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.5

Multiplique $x^{5}$ por $x^{6}$ somando os expoentes.

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Etapa 4.16.20.5.5.1

Mova $x^{6}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 8100 \cdot (2646 (x^{6} x^{5})) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.5.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 8100 \cdot (2646 x^{6 + 5}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.5.3

Some $6$ e $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 8100 \cdot (2646 x^{11}) + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.6

Multiplique $8100$ por $2646$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 8100 \cdot (4116 x^{5} x^{3}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.7

Multiplique $x^{5}$ por $x^{3}$ somando os expoentes.

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Etapa 4.16.20.5.7.1

Mova $x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 8100 \cdot (4116 (x^{3} x^{5})) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.7.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 8100 \cdot (4116 x^{3 + 5}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.7.3

Some $3$ e $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 8100 \cdot (4116 x^{8}) + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.5.8

Multiplique $8100$ por $4116$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 {(3 x^{3} + 7)}^{5} x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.6

Use o teorema binomial.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 ({(3 x^{3})}^{5} + 5 {(3 x^{3})}^{4} \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7

Simplifique cada termo.

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Etapa 4.16.20.7.1

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (3^{5} {(x^{3})}^{5} + 5 {(3 x^{3})}^{4} \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.2

Eleve $3$ à potência de $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 {(x^{3})}^{5} + 5 {(3 x^{3})}^{4} \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.3

Multiplique os expoentes em ${(x^{3})}^{5}$ .

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Etapa 4.16.20.7.3.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{3 \cdot 5} + 5 {(3 x^{3})}^{4} \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.3.2

Multiplique $3$ por $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 5 {(3 x^{3})}^{4} \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.4

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 5 (3^{4} {(x^{3})}^{4}) \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.5

Eleve $3$ à potência de $4$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 5 (81 {(x^{3})}^{4}) \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.6

Multiplique os expoentes em ${(x^{3})}^{4}$ .

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Etapa 4.16.20.7.6.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 5 (81 x^{3 \cdot 4}) \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.6.2

Multiplique $3$ por $4$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 5 (81 x^{12}) \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.7

Multiplique $81$ por $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 405 x^{12} \cdot 7 + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.8

Multiplique $7$ por $405$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 10 {(3 x^{3})}^{3} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.9

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 10 (3^{3} {(x^{3})}^{3}) \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.10

Eleve $3$ à potência de $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 10 (27 {(x^{3})}^{3}) \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.11

Multiplique os expoentes em ${(x^{3})}^{3}$ .

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Etapa 4.16.20.7.11.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 10 (27 x^{3 \cdot 3}) \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.11.2

Multiplique $3$ por $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 10 (27 x^{9}) \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.12

Multiplique $27$ por $10$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 270 x^{9} \cdot 7^{2} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.13

Eleve $7$ à potência de $2$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 270 x^{9} \cdot 49 + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.14

Multiplique $49$ por $270$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 10 {(3 x^{3})}^{2} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.15

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 10 (3^{2} {(x^{3})}^{2}) \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.16

Eleve $3$ à potência de $2$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 10 (9 {(x^{3})}^{2}) \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.17

Multiplique os expoentes em ${(x^{3})}^{2}$ .

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Etapa 4.16.20.7.17.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 10 (9 x^{3 \cdot 2}) \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.17.2

Multiplique $3$ por $2$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 10 (9 x^{6}) \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.18

Multiplique $9$ por $10$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 90 x^{6} \cdot 7^{3} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.19

Eleve $7$ à potência de $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 90 x^{6} \cdot 343 + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.20

Multiplique $343$ por $90$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 30870 x^{6} + 5 (3 x^{3}) \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.21

Multiplique $3$ por $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 30870 x^{6} + 15 x^{3} \cdot 7^{4} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.22

Eleve $7$ à potência de $4$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 30870 x^{6} + 15 x^{3} \cdot 2401 + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.23

Multiplique $2401$ por $15$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 30870 x^{6} + 36015 x^{3} + 7^{5}) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.7.24

Eleve $7$ à potência de $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 360 (243 x^{15} + 2835 x^{12} + 13230 x^{9} + 30870 x^{6} + 36015 x^{3} + 16807) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.8

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + (360 (243 x^{15}) + 360 (2835 x^{12}) + 360 (13230 x^{9}) + 360 (30870 x^{6}) + 360 (36015 x^{3}) + 360 \cdot 16807) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.9

Simplifique.

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Etapa 4.16.20.9.1

Multiplique $243$ por $360$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + (87480 x^{15} + 360 (2835 x^{12}) + 360 (13230 x^{9}) + 360 (30870 x^{6}) + 360 (36015 x^{3}) + 360 \cdot 16807) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.9.2

Multiplique $2835$ por $360$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + (87480 x^{15} + 1020600 x^{12} + 360 (13230 x^{9}) + 360 (30870 x^{6}) + 360 (36015 x^{3}) + 360 \cdot 16807) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.9.3

Multiplique $13230$ por $360$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + (87480 x^{15} + 1020600 x^{12} + 4762800 x^{9} + 360 (30870 x^{6}) + 360 (36015 x^{3}) + 360 \cdot 16807) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.9.4

Multiplique $30870$ por $360$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + (87480 x^{15} + 1020600 x^{12} + 4762800 x^{9} + 11113200 x^{6} + 360 (36015 x^{3}) + 360 \cdot 16807) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.9.5

Multiplique $36015$ por $360$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + (87480 x^{15} + 1020600 x^{12} + 4762800 x^{9} + 11113200 x^{6} + 12965400 x^{3} + 360 \cdot 16807) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.9.6

Multiplique $360$ por $16807$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + (87480 x^{15} + 1020600 x^{12} + 4762800 x^{9} + 11113200 x^{6} + 12965400 x^{3} + 6050520) x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.10

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{15} x^{2} + 1020600 x^{12} x^{2} + 4762800 x^{9} x^{2} + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11

Simplifique.

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Etapa 4.16.20.11.1

Multiplique $x^{15}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.11.1.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 (x^{2} x^{15}) + 1020600 x^{12} x^{2} + 4762800 x^{9} x^{2} + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.1.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{2 + 15} + 1020600 x^{12} x^{2} + 4762800 x^{9} x^{2} + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.1.3

Some $2$ e $15$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{12} x^{2} + 4762800 x^{9} x^{2} + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.2

Multiplique $x^{12}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.11.2.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 (x^{2} x^{12}) + 4762800 x^{9} x^{2} + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{2 + 12} + 4762800 x^{9} x^{2} + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.2.3

Some $2$ e $12$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{9} x^{2} + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.3

Multiplique $x^{9}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.11.3.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 (x^{2} x^{9}) + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.3.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{2 + 9} + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.3.3

Some $2$ e $9$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{6} x^{2} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.4

Multiplique $x^{6}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.11.4.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 (x^{2} x^{6}) + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.4.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{2 + 6} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.4.3

Some $2$ e $6$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{3} x^{2} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.5

Multiplique $x^{3}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.11.5.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 (x^{2} x^{3}) + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.5.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{2 + 3} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} {(3 x^{3} + 7)}^{3} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.11.5.3

Some $2$ e $3$ .

Etapa 4.16.20.12

Simplifique cada termo.

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Etapa 4.16.20.12.1

Use o teorema binomial.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} ({(3 x^{3})}^{3} + 3 {(3 x^{3})}^{2} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2

Simplifique cada termo.

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Etapa 4.16.20.12.2.1

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (3^{3} {(x^{3})}^{3} + 3 {(3 x^{3})}^{2} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.2

Eleve $3$ à potência de $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 {(x^{3})}^{3} + 3 {(3 x^{3})}^{2} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.3

Multiplique os expoentes em ${(x^{3})}^{3}$ .

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Etapa 4.16.20.12.2.3.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{3 \cdot 3} + 3 {(3 x^{3})}^{2} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.3.2

Multiplique $3$ por $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 3 {(3 x^{3})}^{2} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.4

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 3 (3^{2} {(x^{3})}^{2}) \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.5

Multiplique $3$ por $3^{2}$ somando os expoentes.

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Etapa 4.16.20.12.2.5.1

Mova $3^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 3^{2} \cdot (3 {(x^{3})}^{2}) \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.5.2

Multiplique $3^{2}$ por $3$ .

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Etapa 4.16.20.12.2.5.2.1

Eleve $3$ à potência de $1$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 3^{2} \cdot (3 {(x^{3})}^{2}) \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.5.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 3^{2 + 1} {(x^{3})}^{2} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.5.3

Some $2$ e $1$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 3^{3} {(x^{3})}^{2} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.6

Eleve $3$ à potência de $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 27 {(x^{3})}^{2} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.7

Multiplique os expoentes em ${(x^{3})}^{2}$ .

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Etapa 4.16.20.12.2.7.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 27 x^{3 \cdot 2} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.7.2

Multiplique $3$ por $2$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 27 x^{6} \cdot 7 + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.8

Multiplique $7$ por $27$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 189 x^{6} + 3 (3 x^{3}) \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.9

Multiplique $3$ por $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 189 x^{6} + 9 x^{3} \cdot 7^{2} + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.10

Eleve $7$ à potência de $2$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9} + 189 x^{6} + 9 x^{3} \cdot 49 + 7^{3}) + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.2.11

Multiplique $49$ por $9$ .

Etapa 4.16.20.12.2.12

Eleve $7$ à potência de $3$ .

Etapa 4.16.20.12.3

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 x^{5} (27 x^{9}) + 1620 x^{5} (189 x^{6}) + 1620 x^{5} (441 x^{3}) + 1620 x^{5} \cdot 343 + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.4

Simplifique.

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Etapa 4.16.20.12.4.1

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 \cdot (27 x^{5} x^{9}) + 1620 x^{5} (189 x^{6}) + 1620 x^{5} (441 x^{3}) + 1620 x^{5} \cdot 343 + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.4.2

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 \cdot (27 x^{5} x^{9}) + 1620 \cdot (189 x^{5} x^{6}) + 1620 x^{5} (441 x^{3}) + 1620 x^{5} \cdot 343 + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.4.3

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 \cdot (27 x^{5} x^{9}) + 1620 \cdot (189 x^{5} x^{6}) + 1620 \cdot (441 x^{5} x^{3}) + 1620 x^{5} \cdot 343 + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.4.4

Multiplique $343$ por $1620$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 \cdot (27 x^{5} x^{9}) + 1620 \cdot (189 x^{5} x^{6}) + 1620 \cdot (441 x^{5} x^{3}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5

Simplifique cada termo.

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Etapa 4.16.20.12.5.1

Multiplique $x^{5}$ por $x^{9}$ somando os expoentes.

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Etapa 4.16.20.12.5.1.1

Mova $x^{9}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 \cdot (27 (x^{9} x^{5})) + 1620 \cdot (189 x^{5} x^{6}) + 1620 \cdot (441 x^{5} x^{3}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.1.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 \cdot (27 x^{9 + 5}) + 1620 \cdot (189 x^{5} x^{6}) + 1620 \cdot (441 x^{5} x^{3}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.1.3

Some $9$ e $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (1620 \cdot (27 x^{14}) + 1620 \cdot (189 x^{5} x^{6}) + 1620 \cdot (441 x^{5} x^{3}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.2

Multiplique $1620$ por $27$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 1620 \cdot (189 x^{5} x^{6}) + 1620 \cdot (441 x^{5} x^{3}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.3

Multiplique $x^{5}$ por $x^{6}$ somando os expoentes.

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Etapa 4.16.20.12.5.3.1

Mova $x^{6}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 1620 \cdot (189 (x^{6} x^{5})) + 1620 \cdot (441 x^{5} x^{3}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.3.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 1620 \cdot (189 x^{6 + 5}) + 1620 \cdot (441 x^{5} x^{3}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.3.3

Some $6$ e $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 1620 \cdot (189 x^{11}) + 1620 \cdot (441 x^{5} x^{3}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.4

Multiplique $1620$ por $189$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 1620 \cdot (441 x^{5} x^{3}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.5

Multiplique $x^{5}$ por $x^{3}$ somando os expoentes.

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Etapa 4.16.20.12.5.5.1

Mova $x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 1620 \cdot (441 (x^{3} x^{5})) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.5.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 1620 \cdot (441 x^{3 + 5}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.5.3

Some $3$ e $5$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 1620 \cdot (441 x^{8}) + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.5.6

Multiplique $1620$ por $441$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 {(3 x^{3} + 7)}^{4} x^{2}))$

Etapa 4.16.20.12.6

Use o teorema binomial.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 ({(3 x^{3})}^{4} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7

Simplifique cada termo.

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Etapa 4.16.20.12.7.1

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (3^{4} {(x^{3})}^{4} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.2

Eleve $3$ à potência de $4$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 {(x^{3})}^{4} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.3

Multiplique os expoentes em ${(x^{3})}^{4}$ .

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Etapa 4.16.20.12.7.3.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{3 \cdot 4} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.3.2

Multiplique $3$ por $4$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 4 {(3 x^{3})}^{3} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.4

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 4 (3^{3} {(x^{3})}^{3}) \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.5

Eleve $3$ à potência de $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 4 (27 {(x^{3})}^{3}) \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.6

Multiplique os expoentes em ${(x^{3})}^{3}$ .

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Etapa 4.16.20.12.7.6.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 4 (27 x^{3 \cdot 3}) \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.6.2

Multiplique $3$ por $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 4 (27 x^{9}) \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.7

Multiplique $27$ por $4$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 108 x^{9} \cdot 7 + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.8

Multiplique $7$ por $108$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 6 {(3 x^{3})}^{2} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.9

Aplique a regra do produto a $3 x^{3}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 6 (3^{2} {(x^{3})}^{2}) \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.10

Eleve $3$ à potência de $2$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 6 (9 {(x^{3})}^{2}) \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.11

Multiplique os expoentes em ${(x^{3})}^{2}$ .

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Etapa 4.16.20.12.7.11.1

Aplique a regra da multiplicação de potências e multiplique os expoentes, ${(a^{m})}^{n} = a^{m n}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 6 (9 x^{3 \cdot 2}) \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.11.2

Multiplique $3$ por $2$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 6 (9 x^{6}) \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.12

Multiplique $9$ por $6$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 54 x^{6} \cdot 7^{2} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.13

Eleve $7$ à potência de $2$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 54 x^{6} \cdot 49 + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.14

Multiplique $49$ por $54$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 2646 x^{6} + 4 (3 x^{3}) \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.15

Multiplique $3$ por $4$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 2646 x^{6} + 12 x^{3} \cdot 7^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.16

Eleve $7$ à potência de $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 2646 x^{6} + 12 x^{3} \cdot 343 + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.17

Multiplique $343$ por $12$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 2646 x^{6} + 4116 x^{3} + 7^{4}) x^{2}))$

Etapa 4.16.20.12.7.18

Eleve $7$ à potência de $4$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 180 (81 x^{12} + 756 x^{9} + 2646 x^{6} + 4116 x^{3} + 2401) x^{2}))$

Etapa 4.16.20.12.8

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + (180 (81 x^{12}) + 180 (756 x^{9}) + 180 (2646 x^{6}) + 180 (4116 x^{3}) + 180 \cdot 2401) x^{2}))$

Etapa 4.16.20.12.9

Simplifique.

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Etapa 4.16.20.12.9.1

Multiplique $81$ por $180$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + (14580 x^{12} + 180 (756 x^{9}) + 180 (2646 x^{6}) + 180 (4116 x^{3}) + 180 \cdot 2401) x^{2}))$

Etapa 4.16.20.12.9.2

Multiplique $756$ por $180$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + (14580 x^{12} + 136080 x^{9} + 180 (2646 x^{6}) + 180 (4116 x^{3}) + 180 \cdot 2401) x^{2}))$

Etapa 4.16.20.12.9.3

Multiplique $2646$ por $180$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + (14580 x^{12} + 136080 x^{9} + 476280 x^{6} + 180 (4116 x^{3}) + 180 \cdot 2401) x^{2}))$

Etapa 4.16.20.12.9.4

Multiplique $4116$ por $180$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + (14580 x^{12} + 136080 x^{9} + 476280 x^{6} + 740880 x^{3} + 180 \cdot 2401) x^{2}))$

Etapa 4.16.20.12.9.5

Multiplique $180$ por $2401$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + (14580 x^{12} + 136080 x^{9} + 476280 x^{6} + 740880 x^{3} + 432180) x^{2}))$

Etapa 4.16.20.12.10

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{12} x^{2} + 136080 x^{9} x^{2} + 476280 x^{6} x^{2} + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11

Simplifique.

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Etapa 4.16.20.12.11.1

Multiplique $x^{12}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.12.11.1.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 (x^{2} x^{12}) + 136080 x^{9} x^{2} + 476280 x^{6} x^{2} + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11.1.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{2 + 12} + 136080 x^{9} x^{2} + 476280 x^{6} x^{2} + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11.1.3

Some $2$ e $12$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 x^{9} x^{2} + 476280 x^{6} x^{2} + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11.2

Multiplique $x^{9}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.12.11.2.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 (x^{2} x^{9}) + 476280 x^{6} x^{2} + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 x^{2 + 9} + 476280 x^{6} x^{2} + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11.2.3

Some $2$ e $9$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 x^{11} + 476280 x^{6} x^{2} + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11.3

Multiplique $x^{6}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.12.11.3.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 x^{11} + 476280 (x^{2} x^{6}) + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11.3.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 x^{11} + 476280 x^{2 + 6} + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11.3.3

Some $2$ e $6$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 x^{11} + 476280 x^{8} + 740880 x^{3} x^{2} + 432180 x^{2}))$

Etapa 4.16.20.12.11.4

Multiplique $x^{3}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.12.11.4.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 x^{11} + 476280 x^{8} + 740880 (x^{2} x^{3}) + 432180 x^{2}))$

Etapa 4.16.20.12.11.4.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 x^{11} + 476280 x^{8} + 740880 x^{2 + 3} + 432180 x^{2}))$

Etapa 4.16.20.12.11.4.3

Some $2$ e $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (43740 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 14580 x^{14} + 136080 x^{11} + 476280 x^{8} + 740880 x^{5} + 432180 x^{2}))$

Etapa 4.16.20.13

Some $43740 x^{14}$ e $14580 x^{14}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (58320 x^{14} + 306180 x^{11} + 714420 x^{8} + 555660 x^{5} + 136080 x^{11} + 476280 x^{8} + 740880 x^{5} + 432180 x^{2}))$

Etapa 4.16.20.14

Some $306180 x^{11}$ e $136080 x^{11}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (58320 x^{14} + 442260 x^{11} + 714420 x^{8} + 555660 x^{5} + 476280 x^{8} + 740880 x^{5} + 432180 x^{2}))$

Etapa 4.16.20.15

Some $714420 x^{8}$ e $476280 x^{8}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + (30 x^{3} + 7) (58320 x^{14} + 442260 x^{11} + 1190700 x^{8} + 555660 x^{5} + 740880 x^{5} + 432180 x^{2}))$

Etapa 4.16.20.16

Some $555660 x^{5}$ e $740880 x^{5}$ .

Etapa 4.16.20.17

Expanda $(30 x^{3} + 7) (58320 x^{14} + 442260 x^{11} + 1190700 x^{8} + 1296540 x^{5} + 432180 x^{2})$ multiplicando cada termo na primeira expressão por cada um dos termos na segunda expressão.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 30 x^{3} (58320 x^{14}) + 30 x^{3} (442260 x^{11}) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18

Simplifique cada termo.

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Etapa 4.16.20.18.1

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 30 \cdot (58320 x^{3} x^{14}) + 30 x^{3} (442260 x^{11}) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.2

Multiplique $x^{3}$ por $x^{14}$ somando os expoentes.

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Etapa 4.16.20.18.2.1

Mova $x^{14}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 30 \cdot (58320 (x^{14} x^{3})) + 30 x^{3} (442260 x^{11}) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.2.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 30 \cdot (58320 x^{14 + 3}) + 30 x^{3} (442260 x^{11}) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.2.3

Some $14$ e $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 30 \cdot (58320 x^{17}) + 30 x^{3} (442260 x^{11}) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.3

Multiplique $30$ por $58320$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 30 x^{3} (442260 x^{11}) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.4

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 30 \cdot (442260 x^{3} x^{11}) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.5

Multiplique $x^{3}$ por $x^{11}$ somando os expoentes.

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Etapa 4.16.20.18.5.1

Mova $x^{11}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 30 \cdot (442260 (x^{11} x^{3})) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.5.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 30 \cdot (442260 x^{11 + 3}) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.5.3

Some $11$ e $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 30 \cdot (442260 x^{14}) + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.6

Multiplique $30$ por $442260$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 30 x^{3} (1190700 x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.7

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 30 \cdot (1190700 x^{3} x^{8}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.8

Multiplique $x^{3}$ por $x^{8}$ somando os expoentes.

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Etapa 4.16.20.18.8.1

Mova $x^{8}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 30 \cdot (1190700 (x^{8} x^{3})) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.8.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 30 \cdot (1190700 x^{8 + 3}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.8.3

Some $8$ e $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 30 \cdot (1190700 x^{11}) + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.9

Multiplique $30$ por $1190700$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 30 x^{3} (1296540 x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.10

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 30 \cdot (1296540 x^{3} x^{5}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.11

Multiplique $x^{3}$ por $x^{5}$ somando os expoentes.

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Etapa 4.16.20.18.11.1

Mova $x^{5}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 30 \cdot (1296540 (x^{5} x^{3})) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.11.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 30 \cdot (1296540 x^{5 + 3}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.11.3

Some $5$ e $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 30 \cdot (1296540 x^{8}) + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.12

Multiplique $30$ por $1296540$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 30 x^{3} (432180 x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.13

Reescreva usando a propriedade comutativa da multiplicação.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 30 \cdot (432180 x^{3} x^{2}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.14

Multiplique $x^{3}$ por $x^{2}$ somando os expoentes.

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Etapa 4.16.20.18.14.1

Mova $x^{2}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 30 \cdot (432180 (x^{2} x^{3})) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.14.2

Use a regra da multiplicação de potências $a^{m} a^{n} = a^{m + n}$ para combinar expoentes.

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 30 \cdot (432180 x^{2 + 3}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.14.3

Some $2$ e $3$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 30 \cdot (432180 x^{5}) + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.15

Multiplique $30$ por $432180$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 12965400 x^{5} + 7 (58320 x^{14}) + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.16

Multiplique $58320$ por $7$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 12965400 x^{5} + 408240 x^{14} + 7 (442260 x^{11}) + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.17

Multiplique $442260$ por $7$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 12965400 x^{5} + 408240 x^{14} + 3095820 x^{11} + 7 (1190700 x^{8}) + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.18

Multiplique $1190700$ por $7$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 12965400 x^{5} + 408240 x^{14} + 3095820 x^{11} + 8334900 x^{8} + 7 (1296540 x^{5}) + 7 (432180 x^{2}))$

Etapa 4.16.20.18.19

Multiplique $1296540$ por $7$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 12965400 x^{5} + 408240 x^{14} + 3095820 x^{11} + 8334900 x^{8} + 9075780 x^{5} + 7 (432180 x^{2}))$

Etapa 4.16.20.18.20

Multiplique $432180$ por $7$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13267800 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 12965400 x^{5} + 408240 x^{14} + 3095820 x^{11} + 8334900 x^{8} + 9075780 x^{5} + 3025260 x^{2})$

Etapa 4.16.20.19

Some $13267800 x^{14}$ e $408240 x^{14}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13676040 x^{14} + 35721000 x^{11} + 38896200 x^{8} + 12965400 x^{5} + 3095820 x^{11} + 8334900 x^{8} + 9075780 x^{5} + 3025260 x^{2})$

Etapa 4.16.20.20

Some $35721000 x^{11}$ e $3095820 x^{11}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13676040 x^{14} + 38816820 x^{11} + 38896200 x^{8} + 12965400 x^{5} + 8334900 x^{8} + 9075780 x^{5} + 3025260 x^{2})$

Etapa 4.16.20.21

Some $38896200 x^{8}$ e $8334900 x^{8}$ .

$f^{4} (x) = 126 (656100 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 87480 x^{17} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13676040 x^{14} + 38816820 x^{11} + 47231100 x^{8} + 12965400 x^{5} + 9075780 x^{5} + 3025260 x^{2})$

Etapa 4.16.20.22

Some $12965400 x^{5}$ e $9075780 x^{5}$ .

Etapa 4.16.21

Some $656100 x^{17}$ e $87480 x^{17}$ .

$f^{4} (x) = 126 (743580 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 1749600 x^{17} + 13676040 x^{14} + 38816820 x^{11} + 47231100 x^{8} + 22041180 x^{5} + 3025260 x^{2})$

Etapa 4.16.22

Some $743580 x^{17}$ e $1749600 x^{17}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 6123600 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 1020600 x^{14} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 13676040 x^{14} + 38816820 x^{11} + 47231100 x^{8} + 22041180 x^{5} + 3025260 x^{2})$

Etapa 4.16.23

Some $6123600 x^{14}$ e $1020600 x^{14}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 7144200 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 13676040 x^{14} + 38816820 x^{11} + 47231100 x^{8} + 22041180 x^{5} + 3025260 x^{2})$

Etapa 4.16.24

Some $7144200 x^{14}$ e $13676040 x^{14}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 20820240 x^{14} + 21432600 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 4762800 x^{11} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 38816820 x^{11} + 47231100 x^{8} + 22041180 x^{5} + 3025260 x^{2})$

Etapa 4.16.25

Some $21432600 x^{11}$ e $4762800 x^{11}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 20820240 x^{14} + 26195400 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 38816820 x^{11} + 47231100 x^{8} + 22041180 x^{5} + 3025260 x^{2})$

Etapa 4.16.26

Some $26195400 x^{11}$ e $38816820 x^{11}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 20820240 x^{14} + 65012220 x^{11} + 33339600 x^{8} + 19448100 x^{5} + 11113200 x^{8} + 12965400 x^{5} + 6050520 x^{2} + 47231100 x^{8} + 22041180 x^{5} + 3025260 x^{2})$

Etapa 4.16.27

Some $33339600 x^{8}$ e $11113200 x^{8}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 20820240 x^{14} + 65012220 x^{11} + 44452800 x^{8} + 19448100 x^{5} + 12965400 x^{5} + 6050520 x^{2} + 47231100 x^{8} + 22041180 x^{5} + 3025260 x^{2})$

Etapa 4.16.28

Some $44452800 x^{8}$ e $47231100 x^{8}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 20820240 x^{14} + 65012220 x^{11} + 91683900 x^{8} + 19448100 x^{5} + 12965400 x^{5} + 6050520 x^{2} + 22041180 x^{5} + 3025260 x^{2})$

Etapa 4.16.29

Some $19448100 x^{5}$ e $12965400 x^{5}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 20820240 x^{14} + 65012220 x^{11} + 91683900 x^{8} + 32413500 x^{5} + 6050520 x^{2} + 22041180 x^{5} + 3025260 x^{2})$

Etapa 4.16.30

Some $32413500 x^{5}$ e $22041180 x^{5}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 20820240 x^{14} + 65012220 x^{11} + 91683900 x^{8} + 54454680 x^{5} + 6050520 x^{2} + 3025260 x^{2})$

Etapa 4.16.31

Some $6050520 x^{2}$ e $3025260 x^{2}$ .

$f^{4} (x) = 126 (2493180 x^{17} + 20820240 x^{14} + 65012220 x^{11} + 91683900 x^{8} + 54454680 x^{5} + 9075780 x^{2})$

Etapa 4.16.32

Aplique a propriedade distributiva.

$f^{4} (x) = 126 (2493180 x^{17}) + 126 (20820240 x^{14}) + 126 (65012220 x^{11}) + 126 (91683900 x^{8}) + 126 (54454680 x^{5}) + 126 (9075780 x^{2})$

Etapa 4.16.33

Simplifique.

Toque para ver mais passagens...

Etapa 4.16.33.1

Multiplique $2493180$ por $126$ .

$f^{4} (x) = 314140680 x^{17} + 126 (20820240 x^{14}) + 126 (65012220 x^{11}) + 126 (91683900 x^{8}) + 126 (54454680 x^{5}) + 126 (9075780 x^{2})$

Etapa 4.16.33.2

Multiplique $20820240$ por $126$ .

$f^{4} (x) = 314140680 x^{17} + 2623350240 x^{14} + 126 (65012220 x^{11}) + 126 (91683900 x^{8}) + 126 (54454680 x^{5}) + 126 (9075780 x^{2})$

Etapa 4.16.33.3

Multiplique $65012220$ por $126$ .

$f^{4} (x) = 314140680 x^{17} + 2623350240 x^{14} + 8191539720 x^{11} + 126 (91683900 x^{8}) + 126 (54454680 x^{5}) + 126 (9075780 x^{2})$

Etapa 4.16.33.4

Multiplique $91683900$ por $126$ .

$f^{4} (x) = 314140680 x^{17} + 2623350240 x^{14} + 8191539720 x^{11} + 11552171400 x^{8} + 126 (54454680 x^{5}) + 126 (9075780 x^{2})$

Etapa 4.16.33.5

Multiplique $54454680$ por $126$ .

$f^{4} (x) = 314140680 x^{17} + 2623350240 x^{14} + 8191539720 x^{11} + 11552171400 x^{8} + 6861289680 x^{5} + 126 (9075780 x^{2})$

Etapa 4.16.33.6

Multiplique $9075780$ por $126$ .

$f^{4} (x) = 314140680 x^{17} + 2623350240 x^{14} + 8191539720 x^{11} + 11552171400 x^{8} + 6861289680 x^{5} + 1143548280 x^{2}$

Etapa 5

A quarta derivada de $f (x)$ com relação a $x$ é $314140680 x^{17} + 2623350240 x^{14} + 8191539720 x^{11} + 11552171400 x^{8} + 6861289680 x^{5} + 1143548280 x^{2}$ .

$314140680 x^{17} + 2623350240 x^{14} + 8191539720 x^{11} + 11552171400 x^{8} + 6861289680 x^{5} + 1143548280 x^{2}$