Cálculo Exemplos

$y = \frac{{(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3}}{{(e^{x} + 1)}^{7}}$

Etapa 1

Diferencie os dois lados da equação.

$\frac{d}{d x} (y) = \frac{d}{d x} (\frac{{(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3}}{{(e^{x} + 1)}^{7}})$

Etapa 2

A derivada de $y$ em relação a $x$ é $y'$ .

$y'$

Etapa 3

Diferencie o lado direito da equação.

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Etapa 3.1

Diferencie usando a regra do quociente, que determina que $\frac{d}{d x} [\frac{f (x)}{g (x)}]$ é $\frac{g (x) \frac{d}{d x} [f (x)] - f (x) \frac{d}{d x} [g (x)]}{{g (x)}^{2}}$ , em que $f (x) = {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3}$ e $g (x) = {(e^{x} + 1)}^{7}$ .

$\frac{{(e^{x} + 1)}^{7} \frac{d}{d x} [{(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3}] - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{({(e^{x} + 1)}^{7})}^{2}}$

Etapa 3.2

Multiplique os expoentes em ${({(e^{x} + 1)}^{7})}^{2}$ .

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Etapa 3.2.1

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

$\frac{{(e^{x} + 1)}^{7} \frac{d}{d x} [{(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3}] - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{7 \cdot 2}}$

Etapa 3.2.2

Multiplique $7$ por $2$ .

$\frac{{(e^{x} + 1)}^{7} \frac{d}{d x} [{(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3}] - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.3

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 $f (x) = {(x^{2} + 1)}^{10}$ e $g (x) = {(x^{2} + 2)}^{3}$ .

$\frac{{(e^{x} + 1)}^{7} ({(x^{2} + 1)}^{10} \frac{d}{d x} [{(x^{2} + 2)}^{3}] + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.4

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

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Etapa 3.4.1

Para aplicar a regra da cadeia, defina $u_{1}$ como $x^{2} + 2$ .

$\frac{{(e^{x} + 1)}^{7} ({(x^{2} + 1)}^{10} (\frac{d}{d u_{1}} [{u_{1}}^{3}] \frac{d}{d x} [x^{2} + 2]) + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.4.2

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 $n = 3$ .

$\frac{{(e^{x} + 1)}^{7} ({(x^{2} + 1)}^{10} (3 {u_{1}}^{2} \frac{d}{d x} [x^{2} + 2]) + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.4.3

Substitua todas as ocorrências de $u_{1}$ por $x^{2} + 2$ .

$\frac{{(e^{x} + 1)}^{7} ({(x^{2} + 1)}^{10} (3 {(x^{2} + 2)}^{2} \frac{d}{d x} [x^{2} + 2]) + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.5

Diferencie.

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Etapa 3.5.1

Mova $3$ para a esquerda de ${(x^{2} + 1)}^{10}$ .

$\frac{{(e^{x} + 1)}^{7} (3 \cdot {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} \frac{d}{d x} [x^{2} + 2] + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.5.2

De acordo com a regra da soma, a derivada de $x^{2} + 2$ com relação a $x$ é $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [2]$ .

$\frac{{(e^{x} + 1)}^{7} (3 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} (\frac{d}{d x} [x^{2}] + \frac{d}{d x} [2]) + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.5.3

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

$\frac{{(e^{x} + 1)}^{7} (3 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} (2 x + \frac{d}{d x} [2]) + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.5.4

Como $2$ é constante em relação a $x$ , a derivada de $2$ em relação a $x$ é $0$ .

$\frac{{(e^{x} + 1)}^{7} (3 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} (2 x + 0) + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.5.5

Simplifique a expressão.

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Etapa 3.5.5.1

Some $2 x$ e $0$ .

$\frac{{(e^{x} + 1)}^{7} (3 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} (2 x) + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.5.5.2

Multiplique $2$ por $3$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + {(x^{2} + 2)}^{3} \frac{d}{d x} [{(x^{2} + 1)}^{10}]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.6

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{10}$ e $g (x) = x^{2} + 1$ .

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Etapa 3.6.1

Para aplicar a regra da cadeia, defina $u_{2}$ como $x^{2} + 1$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + {(x^{2} + 2)}^{3} (\frac{d}{d u_{2}} [{u_{2}}^{10}] \frac{d}{d x} [x^{2} + 1])) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.6.2

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 $n = 10$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + {(x^{2} + 2)}^{3} (10 {u_{2}}^{9} \frac{d}{d x} [x^{2} + 1])) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.6.3

Substitua todas as ocorrências de $u_{2}$ por $x^{2} + 1$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + {(x^{2} + 2)}^{3} (10 {(x^{2} + 1)}^{9} \frac{d}{d x} [x^{2} + 1])) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.7

Diferencie.

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Etapa 3.7.1

Mova $10$ para a esquerda de ${(x^{2} + 2)}^{3}$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 10 \cdot {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} \frac{d}{d x} [x^{2} + 1]) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.7.2

De acordo com a regra da soma, a derivada de $x^{2} + 1$ com relação a $x$ é $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [1]$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 10 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} (\frac{d}{d x} [x^{2}] + \frac{d}{d x} [1])) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.7.3

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

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 10 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} (2 x + \frac{d}{d x} [1])) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.7.4

Como $1$ é constante em relação a $x$ , a derivada de $1$ em relação a $x$ é $0$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 10 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} (2 x + 0)) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.7.5

Simplifique a expressão.

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Etapa 3.7.5.1

Some $2 x$ e $0$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 10 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} (2 x)) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

Etapa 3.7.5.2

Multiplique $2$ por $10$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} \frac{d}{d x} [{(e^{x} + 1)}^{7}]}{{(e^{x} + 1)}^{14}}$

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 $f (x) = x^{7}$ e $g (x) = e^{x} + 1$ .

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Etapa 3.8.1

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

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (\frac{d}{d u_{3}} [{u_{3}}^{7}] \frac{d}{d x} [e^{x} + 1])}{{(e^{x} + 1)}^{14}}$

Etapa 3.8.2

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 $n = 7$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (7 {u_{3}}^{6} \frac{d}{d x} [e^{x} + 1])}{{(e^{x} + 1)}^{14}}$

Etapa 3.8.3

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

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (7 {(e^{x} + 1)}^{6} \frac{d}{d x} [e^{x} + 1])}{{(e^{x} + 1)}^{14}}$

Etapa 3.9

Simplifique com fatoração.

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Etapa 3.9.1

Multiplique $7$ por $- 1$ .

$\frac{{(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} ({(e^{x} + 1)}^{6} \frac{d}{d x} [e^{x} + 1])}{{(e^{x} + 1)}^{14}}$

Etapa 3.9.2

Fatore ${(e^{x} + 1)}^{6}$ de ${(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} ({(e^{x} + 1)}^{6} \frac{d}{d x} [e^{x} + 1])$ .

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Etapa 3.9.2.1

Fatore ${(e^{x} + 1)}^{6}$ de ${(e^{x} + 1)}^{7} (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x)$ .

$\frac{{(e^{x} + 1)}^{6} ((e^{x} + 1) (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x)) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} ({(e^{x} + 1)}^{6} \frac{d}{d x} [e^{x} + 1])}{{(e^{x} + 1)}^{14}}$

Etapa 3.9.2.2

Fatore ${(e^{x} + 1)}^{6}$ de $- 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} ({(e^{x} + 1)}^{6} \frac{d}{d x} [e^{x} + 1])$ .

$\frac{{(e^{x} + 1)}^{6} ((e^{x} + 1) (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x)) + {(e^{x} + 1)}^{6} (- 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (\frac{d}{d x} [e^{x} + 1]))}{{(e^{x} + 1)}^{14}}$

Etapa 3.9.2.3

Fatore ${(e^{x} + 1)}^{6}$ de ${(e^{x} + 1)}^{6} ((e^{x} + 1) (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x)) + {(e^{x} + 1)}^{6} (- 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (\frac{d}{d x} [e^{x} + 1]))$ .

$\frac{{(e^{x} + 1)}^{6} ((e^{x} + 1) (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (\frac{d}{d x} [e^{x} + 1]))}{{(e^{x} + 1)}^{14}}$

Etapa 3.10

Cancele os fatores comuns.

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Etapa 3.10.1

Fatore ${(e^{x} + 1)}^{6}$ de ${(e^{x} + 1)}^{14}$ .

Etapa 3.10.2

Cancele o fator comum.

Etapa 3.10.3

Reescreva a expressão.

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (\frac{d}{d x} [e^{x} + 1])}{{(e^{x} + 1)}^{8}}$

Etapa 3.11

De acordo com a regra da soma, a derivada de $e^{x} + 1$ com relação a $x$ é $\frac{d}{d x} [e^{x}] + \frac{d}{d x} [1]$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (\frac{d}{d x} [e^{x}] + \frac{d}{d x} [1])}{{(e^{x} + 1)}^{8}}$

Etapa 3.12

Diferencie usando a regra exponencial, que determina que $\frac{d}{d x} [a^{x}]$ é $a^{x} \ln (a)$ , em que $a$ = $e$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (e^{x} + \frac{d}{d x} [1])}{{(e^{x} + 1)}^{8}}$

Etapa 3.13

Diferencie usando a regra da constante.

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Etapa 3.13.1

Como $1$ é constante em relação a $x$ , a derivada de $1$ em relação a $x$ é $0$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} (e^{x} + 0)}{{(e^{x} + 1)}^{8}}$

Etapa 3.13.2

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{2} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14

Simplifique o numerador.

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Etapa 3.14.1

Simplifique cada termo.

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Etapa 3.14.1.1

Reescreva ${(x^{2} + 2)}^{2}$ como $(x^{2} + 2) (x^{2} + 2)$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} ((x^{2} + 2) (x^{2} + 2)) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.2

Expanda $(x^{2} + 2) (x^{2} + 2)$ usando o método FOIL.

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Etapa 3.14.1.2.1

Aplique a propriedade distributiva.

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x^{2} (x^{2} + 2) + 2 (x^{2} + 2)) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.2.2

Aplique a propriedade distributiva.

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x^{2} x^{2} + x^{2} \cdot 2 + 2 (x^{2} + 2)) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.2.3

Aplique a propriedade distributiva.

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x^{2} x^{2} + x^{2} \cdot 2 + 2 x^{2} + 2 \cdot 2) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.3

Simplifique e combine termos semelhantes.

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Etapa 3.14.1.3.1

Simplifique cada termo.

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Etapa 3.14.1.3.1.1

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

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Etapa 3.14.1.3.1.1.1

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x^{2 + 2} + x^{2} \cdot 2 + 2 x^{2} + 2 \cdot 2) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.3.1.1.2

Some $2$ e $2$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x^{4} + x^{2} \cdot 2 + 2 x^{2} + 2 \cdot 2) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.3.1.2

Mova $2$ para a esquerda de $x^{2}$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x^{4} + 2 \cdot x^{2} + 2 x^{2} + 2 \cdot 2) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.3.1.3

Multiplique $2$ por $2$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x^{4} + 2 x^{2} + 2 x^{2} + 4) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.3.2

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x^{4} + 4 x^{2} + 4) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.4

Aplique a propriedade distributiva.

$\frac{(e^{x} + 1) ((6 {(x^{2} + 1)}^{10} x^{4} + 6 {(x^{2} + 1)}^{10} (4 x^{2}) + 6 {(x^{2} + 1)}^{10} \cdot 4) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.5

Simplifique.

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Etapa 3.14.1.5.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{(e^{x} + 1) ((6 {(x^{2} + 1)}^{10} x^{4} + 6 \cdot 4 {(x^{2} + 1)}^{10} x^{2} + 6 {(x^{2} + 1)}^{10} \cdot 4) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.5.2

Multiplique $4$ por $6$ .

$\frac{(e^{x} + 1) ((6 {(x^{2} + 1)}^{10} x^{4} + 6 \cdot 4 {(x^{2} + 1)}^{10} x^{2} + 24 {(x^{2} + 1)}^{10}) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.6

Multiplique $6$ por $4$ .

$\frac{(e^{x} + 1) ((6 {(x^{2} + 1)}^{10} x^{4} + 24 {(x^{2} + 1)}^{10} x^{2} + 24 {(x^{2} + 1)}^{10}) x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.7

Aplique a propriedade distributiva.

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{4} x + 24 {(x^{2} + 1)}^{10} x^{2} x + 24 {(x^{2} + 1)}^{10} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.8

Simplifique.

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Etapa 3.14.1.8.1

Multiplique $x^{4}$ por $x$ somando os expoentes.

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Etapa 3.14.1.8.1.1

Mova $x$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x \cdot x^{4}) + 24 {(x^{2} + 1)}^{10} x^{2} x + 24 {(x^{2} + 1)}^{10} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.8.1.2

Multiplique $x$ por $x^{4}$ .

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Etapa 3.14.1.8.1.2.1

Eleve $x$ à potência de $1$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} (x^{1} x^{4}) + 24 {(x^{2} + 1)}^{10} x^{2} x + 24 {(x^{2} + 1)}^{10} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.8.1.2.2

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{1 + 4} + 24 {(x^{2} + 1)}^{10} x^{2} x + 24 {(x^{2} + 1)}^{10} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.8.1.3

Some $1$ e $4$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{2} x + 24 {(x^{2} + 1)}^{10} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.8.2

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

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Etapa 3.14.1.8.2.1

Mova $x$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} (x \cdot x^{2}) + 24 {(x^{2} + 1)}^{10} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.8.2.2

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

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Etapa 3.14.1.8.2.2.1

Eleve $x$ à potência de $1$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} (x^{1} x^{2}) + 24 {(x^{2} + 1)}^{10} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.8.2.2.2

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{1 + 2} + 24 {(x^{2} + 1)}^{10} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.8.2.3

Some $1$ e $2$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 {(x^{2} + 2)}^{3} {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.9

Use o teorema binomial.

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 ({(x^{2})}^{3} + 3 {(x^{2})}^{2} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.10

Simplifique cada termo.

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Etapa 3.14.1.10.1

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

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Etapa 3.14.1.10.1.1

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x^{2 \cdot 3} + 3 {(x^{2})}^{2} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.10.1.2

Multiplique $2$ por $3$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x^{6} + 3 {(x^{2})}^{2} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.10.2

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

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Etapa 3.14.1.10.2.1

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x^{6} + 3 x^{2 \cdot 2} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.10.2.2

Multiplique $2$ por $2$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x^{6} + 3 x^{4} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.10.3

Multiplique $2$ por $3$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x^{6} + 6 x^{4} + 3 x^{2} \cdot 2^{2} + 2^{3}) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.10.4

Eleve $2$ à potência de $2$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x^{6} + 6 x^{4} + 3 x^{2} \cdot 4 + 2^{3}) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.10.5

Multiplique $4$ por $3$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x^{6} + 6 x^{4} + 12 x^{2} + 2^{3}) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.10.6

Eleve $2$ à potência de $3$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x^{6} + 6 x^{4} + 12 x^{2} + 8) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.11

Aplique a propriedade distributiva.

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + (20 x^{6} + 20 (6 x^{4}) + 20 (12 x^{2}) + 20 \cdot 8) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.12

Simplifique.

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Etapa 3.14.1.12.1

Multiplique $6$ por $20$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + (20 x^{6} + 120 x^{4} + 20 (12 x^{2}) + 20 \cdot 8) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.12.2

Multiplique $12$ por $20$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + (20 x^{6} + 120 x^{4} + 240 x^{2} + 20 \cdot 8) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.12.3

Multiplique $20$ por $8$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + (20 x^{6} + 120 x^{4} + 240 x^{2} + 160) {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.13

Aplique a propriedade distributiva.

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + (20 x^{6} {(x^{2} + 1)}^{9} + 120 x^{4} {(x^{2} + 1)}^{9} + 240 x^{2} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9}) x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.14

Aplique a propriedade distributiva.

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{6} {(x^{2} + 1)}^{9} x + 120 x^{4} {(x^{2} + 1)}^{9} x + 240 x^{2} {(x^{2} + 1)}^{9} x + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15

Simplifique.

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Etapa 3.14.1.15.1

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

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Etapa 3.14.1.15.1.1

Mova $x$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x \cdot x^{6}) {(x^{2} + 1)}^{9} + 120 x^{4} {(x^{2} + 1)}^{9} x + 240 x^{2} {(x^{2} + 1)}^{9} x + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.1.2

Multiplique $x$ por $x^{6}$ .

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Etapa 3.14.1.15.1.2.1

Eleve $x$ à potência de $1$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 (x^{1} x^{6}) {(x^{2} + 1)}^{9} + 120 x^{4} {(x^{2} + 1)}^{9} x + 240 x^{2} {(x^{2} + 1)}^{9} x + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.1.2.2

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{1 + 6} {(x^{2} + 1)}^{9} + 120 x^{4} {(x^{2} + 1)}^{9} x + 240 x^{2} {(x^{2} + 1)}^{9} x + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.1.3

Some $1$ e $6$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{4} {(x^{2} + 1)}^{9} x + 240 x^{2} {(x^{2} + 1)}^{9} x + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.2

Multiplique $x^{4}$ por $x$ somando os expoentes.

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Etapa 3.14.1.15.2.1

Mova $x$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 (x \cdot x^{4}) {(x^{2} + 1)}^{9} + 240 x^{2} {(x^{2} + 1)}^{9} x + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.2.2

Multiplique $x$ por $x^{4}$ .

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Etapa 3.14.1.15.2.2.1

Eleve $x$ à potência de $1$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 (x^{1} x^{4}) {(x^{2} + 1)}^{9} + 240 x^{2} {(x^{2} + 1)}^{9} x + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.2.2.2

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{1 + 4} {(x^{2} + 1)}^{9} + 240 x^{2} {(x^{2} + 1)}^{9} x + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.2.3

Some $1$ e $4$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{2} {(x^{2} + 1)}^{9} x + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.3

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

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Etapa 3.14.1.15.3.1

Mova $x$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 (x \cdot x^{2}) {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.3.2

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

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Etapa 3.14.1.15.3.2.1

Eleve $x$ à potência de $1$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 (x^{1} x^{2}) {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.3.2.2

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

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{1 + 2} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.1.15.3.3

Some $1$ e $2$ .

$\frac{(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.2

Expanda $(e^{x} + 1) (6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x)$ multiplicando cada termo na primeira expressão por cada um dos termos na segunda expressão.

$\frac{e^{x} (6 {(x^{2} + 1)}^{10} x^{5}) + e^{x} (24 {(x^{2} + 1)}^{10} x^{3}) + e^{x} (24 {(x^{2} + 1)}^{10} x) + e^{x} (20 x^{7} {(x^{2} + 1)}^{9}) + e^{x} (120 x^{5} {(x^{2} + 1)}^{9}) + e^{x} (240 x^{3} {(x^{2} + 1)}^{9}) + e^{x} (160 {(x^{2} + 1)}^{9} x) + 1 (6 {(x^{2} + 1)}^{10} x^{5}) + 1 (24 {(x^{2} + 1)}^{10} x^{3}) + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3

Simplifique cada termo.

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Etapa 3.14.3.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + e^{x} (24 {(x^{2} + 1)}^{10} x^{3}) + e^{x} (24 {(x^{2} + 1)}^{10} x) + e^{x} (20 x^{7} {(x^{2} + 1)}^{9}) + e^{x} (120 x^{5} {(x^{2} + 1)}^{9}) + e^{x} (240 x^{3} {(x^{2} + 1)}^{9}) + e^{x} (160 {(x^{2} + 1)}^{9} x) + 1 (6 {(x^{2} + 1)}^{10} x^{5}) + 1 (24 {(x^{2} + 1)}^{10} x^{3}) + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.2

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + e^{x} (24 {(x^{2} + 1)}^{10} x) + e^{x} (20 x^{7} {(x^{2} + 1)}^{9}) + e^{x} (120 x^{5} {(x^{2} + 1)}^{9}) + e^{x} (240 x^{3} {(x^{2} + 1)}^{9}) + e^{x} (160 {(x^{2} + 1)}^{9} x) + 1 (6 {(x^{2} + 1)}^{10} x^{5}) + 1 (24 {(x^{2} + 1)}^{10} x^{3}) + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.3

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + e^{x} (20 x^{7} {(x^{2} + 1)}^{9}) + e^{x} (120 x^{5} {(x^{2} + 1)}^{9}) + e^{x} (240 x^{3} {(x^{2} + 1)}^{9}) + e^{x} (160 {(x^{2} + 1)}^{9} x) + 1 (6 {(x^{2} + 1)}^{10} x^{5}) + 1 (24 {(x^{2} + 1)}^{10} x^{3}) + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.4

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + e^{x} (120 x^{5} {(x^{2} + 1)}^{9}) + e^{x} (240 x^{3} {(x^{2} + 1)}^{9}) + e^{x} (160 {(x^{2} + 1)}^{9} x) + 1 (6 {(x^{2} + 1)}^{10} x^{5}) + 1 (24 {(x^{2} + 1)}^{10} x^{3}) + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.5

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + e^{x} (240 x^{3} {(x^{2} + 1)}^{9}) + e^{x} (160 {(x^{2} + 1)}^{9} x) + 1 (6 {(x^{2} + 1)}^{10} x^{5}) + 1 (24 {(x^{2} + 1)}^{10} x^{3}) + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.6

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + e^{x} (160 {(x^{2} + 1)}^{9} x) + 1 (6 {(x^{2} + 1)}^{10} x^{5}) + 1 (24 {(x^{2} + 1)}^{10} x^{3}) + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.7

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 1 (6 {(x^{2} + 1)}^{10} x^{5}) + 1 (24 {(x^{2} + 1)}^{10} x^{3}) + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.8

Multiplique $6 {(x^{2} + 1)}^{10} x^{5}$ por $1$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 1 (24 {(x^{2} + 1)}^{10} x^{3}) + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.9

Multiplique $24 {(x^{2} + 1)}^{10} x^{3}$ por $1$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 1 (24 {(x^{2} + 1)}^{10} x) + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.10

Multiplique $24 {(x^{2} + 1)}^{10} x$ por $1$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 1 (20 x^{7} {(x^{2} + 1)}^{9}) + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.11

Multiplique $20 x^{7} {(x^{2} + 1)}^{9}$ por $1$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 1 (120 x^{5} {(x^{2} + 1)}^{9}) + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.12

Multiplique $120 x^{5} {(x^{2} + 1)}^{9}$ por $1$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 1 (240 x^{3} {(x^{2} + 1)}^{9}) + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.13

Multiplique $240 x^{3} {(x^{2} + 1)}^{9}$ por $1$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 1 (160 {(x^{2} + 1)}^{9} x) - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.3.14

Multiplique $160 {(x^{2} + 1)}^{9} x$ por $1$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} {(x^{2} + 2)}^{3} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.4

Use o teorema binomial.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} ({(x^{2})}^{3} + 3 {(x^{2})}^{2} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.5

Simplifique cada termo.

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Etapa 3.14.5.1

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

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Etapa 3.14.5.1.1

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

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} (x^{2 \cdot 3} + 3 {(x^{2})}^{2} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.5.1.2

Multiplique $2$ por $3$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} (x^{6} + 3 {(x^{2})}^{2} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.5.2

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

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Etapa 3.14.5.2.1

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

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} (x^{6} + 3 x^{2 \cdot 2} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.5.2.2

Multiplique $2$ por $2$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} (x^{6} + 3 x^{4} \cdot 2 + 3 x^{2} \cdot 2^{2} + 2^{3}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.5.3

Multiplique $2$ por $3$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} (x^{6} + 6 x^{4} + 3 x^{2} \cdot 2^{2} + 2^{3}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.5.4

Eleve $2$ à potência de $2$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} (x^{6} + 6 x^{4} + 3 x^{2} \cdot 4 + 2^{3}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.5.5

Multiplique $4$ por $3$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} (x^{6} + 6 x^{4} + 12 x^{2} + 2^{3}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.5.6

Eleve $2$ à potência de $3$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} (x^{6} + 6 x^{4} + 12 x^{2} + 8) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.6

Aplique a propriedade distributiva.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x + (- 7 {(x^{2} + 1)}^{10} x^{6} - 7 {(x^{2} + 1)}^{10} (6 x^{4}) - 7 {(x^{2} + 1)}^{10} (12 x^{2}) - 7 {(x^{2} + 1)}^{10} \cdot 8) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.7

Simplifique.

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Etapa 3.14.7.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x + (- 7 {(x^{2} + 1)}^{10} x^{6} - 7 \cdot 6 {(x^{2} + 1)}^{10} x^{4} - 7 {(x^{2} + 1)}^{10} (12 x^{2}) - 7 {(x^{2} + 1)}^{10} \cdot 8) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.7.2

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x + (- 7 {(x^{2} + 1)}^{10} x^{6} - 7 \cdot 6 {(x^{2} + 1)}^{10} x^{4} - 7 \cdot 12 {(x^{2} + 1)}^{10} x^{2} - 7 {(x^{2} + 1)}^{10} \cdot 8) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.7.3

Multiplique $8$ por $- 7$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x + (- 7 {(x^{2} + 1)}^{10} x^{6} - 7 \cdot 6 {(x^{2} + 1)}^{10} x^{4} - 7 \cdot 12 {(x^{2} + 1)}^{10} x^{2} - 56 {(x^{2} + 1)}^{10}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.8

Simplifique cada termo.

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Etapa 3.14.8.1

Multiplique $- 7$ por $6$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x + (- 7 {(x^{2} + 1)}^{10} x^{6} - 42 {(x^{2} + 1)}^{10} x^{4} - 7 \cdot 12 {(x^{2} + 1)}^{10} x^{2} - 56 {(x^{2} + 1)}^{10}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.8.2

Multiplique $- 7$ por $12$ .

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x + (- 7 {(x^{2} + 1)}^{10} x^{6} - 42 {(x^{2} + 1)}^{10} x^{4} - 84 {(x^{2} + 1)}^{10} x^{2} - 56 {(x^{2} + 1)}^{10}) e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.9

Aplique a propriedade distributiva.

$\frac{6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10

Reescreva $6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}$ em uma forma fatorada.

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Etapa 3.14.10.1

Fatore ${(x^{2} + 1)}^{9}$ de $6 e^{x} ({(x^{2} + 1)}^{10} x^{5}) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}$ .

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Etapa 3.14.10.1.1

Fatore ${(x^{2} + 1)}^{9}$ de $6 e^{x} ({(x^{2} + 1)}^{10} x^{5})$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + 24 e^{x} ({(x^{2} + 1)}^{10} x^{3}) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.2

Fatore ${(x^{2} + 1)}^{9}$ de $24 e^{x} ({(x^{2} + 1)}^{10} x^{3})$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + 24 e^{x} ({(x^{2} + 1)}^{10} x) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.3

Fatore ${(x^{2} + 1)}^{9}$ de $24 e^{x} ({(x^{2} + 1)}^{10} x)$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + 20 e^{x} (x^{7} {(x^{2} + 1)}^{9}) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.4

Fatore ${(x^{2} + 1)}^{9}$ de $20 e^{x} (x^{7} {(x^{2} + 1)}^{9})$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + 120 e^{x} (x^{5} {(x^{2} + 1)}^{9}) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.5

Fatore ${(x^{2} + 1)}^{9}$ de $120 e^{x} (x^{5} {(x^{2} + 1)}^{9})$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + 240 e^{x} (x^{3} {(x^{2} + 1)}^{9}) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.6

Fatore ${(x^{2} + 1)}^{9}$ de $240 e^{x} (x^{3} {(x^{2} + 1)}^{9})$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + 160 e^{x} ({(x^{2} + 1)}^{9} x) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.7

Fatore ${(x^{2} + 1)}^{9}$ de $160 e^{x} ({(x^{2} + 1)}^{9} x)$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + 6 {(x^{2} + 1)}^{10} x^{5} + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.8

Fatore ${(x^{2} + 1)}^{9}$ de $6 {(x^{2} + 1)}^{10} x^{5}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + 24 {(x^{2} + 1)}^{10} x^{3} + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.9

Fatore ${(x^{2} + 1)}^{9}$ de $24 {(x^{2} + 1)}^{10} x^{3}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + 24 {(x^{2} + 1)}^{10} x + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.10

Fatore ${(x^{2} + 1)}^{9}$ de $24 {(x^{2} + 1)}^{10} x$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + 20 x^{7} {(x^{2} + 1)}^{9} + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.11

Fatore ${(x^{2} + 1)}^{9}$ de $20 x^{7} {(x^{2} + 1)}^{9}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + 120 x^{5} {(x^{2} + 1)}^{9} + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.12

Fatore ${(x^{2} + 1)}^{9}$ de $120 x^{5} {(x^{2} + 1)}^{9}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + 240 x^{3} {(x^{2} + 1)}^{9} + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.13

Fatore ${(x^{2} + 1)}^{9}$ de $240 x^{3} {(x^{2} + 1)}^{9}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + 160 {(x^{2} + 1)}^{9} x - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.14

Fatore ${(x^{2} + 1)}^{9}$ de $160 {(x^{2} + 1)}^{9} x$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) - 7 {(x^{2} + 1)}^{10} x^{6} e^{x} - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.15

Fatore ${(x^{2} + 1)}^{9}$ de $- 7 {(x^{2} + 1)}^{10} x^{6} e^{x}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) - 42 {(x^{2} + 1)}^{10} x^{4} e^{x} - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.16

Fatore ${(x^{2} + 1)}^{9}$ de $- 42 {(x^{2} + 1)}^{10} x^{4} e^{x}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) - 84 {(x^{2} + 1)}^{10} x^{2} e^{x} - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.17

Fatore ${(x^{2} + 1)}^{9}$ de $- 84 {(x^{2} + 1)}^{10} x^{2} e^{x}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) - 56 {(x^{2} + 1)}^{10} e^{x}}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.18

Fatore ${(x^{2} + 1)}^{9}$ de $- 56 {(x^{2} + 1)}^{10} e^{x}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.19

Fatore ${(x^{2} + 1)}^{9}$ de ${(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x^{3}))$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.20

Fatore ${(x^{2} + 1)}^{9}$ de ${(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3})) + {(x^{2} + 1)}^{9} (24 e^{x} ((x^{2} + 1) x))$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.21

Fatore ${(x^{2} + 1)}^{9}$ de ${(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x)) + {(x^{2} + 1)}^{9} (20 e^{x} (x^{7}))$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.22

Fatore ${(x^{2} + 1)}^{9}$ de ${(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7})) + {(x^{2} + 1)}^{9} (120 e^{x} (x^{5}))$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.23

Fatore ${(x^{2} + 1)}^{9}$ de ${(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5})) + {(x^{2} + 1)}^{9} (240 e^{x} (x^{3}))$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3})) + {(x^{2} + 1)}^{9} (160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.24

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x)) + {(x^{2} + 1)}^{9} (6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.25

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.26

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3}) + {(x^{2} + 1)}^{9} (24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.27

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x) + {(x^{2} + 1)}^{9} (20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.28

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.29

Fatore ${(x^{2} + 1)}^{9}$ de ${(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7}) + {(x^{2} + 1)}^{9} (120 x^{5})$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5}) + {(x^{2} + 1)}^{9} (240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.30

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3}) + {(x^{2} + 1)}^{9} (160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.31

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x) + {(x^{2} + 1)}^{9} (- 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.32

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x}) + {(x^{2} + 1)}^{9} (- 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.33

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x}) + {(x^{2} + 1)}^{9} (- 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.34

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} ((x^{2} + 1) x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x}) + {(x^{2} + 1)}^{9} (- 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.1.35

Etapa 3.14.10.2

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} (x^{2} x^{5} + 1 x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.3

Multiplique $x^{2}$ por $x^{5}$ somando os expoentes.

Toque para ver mais passagens...

Etapa 3.14.10.3.1

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

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} (x^{2 + 5} + 1 x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.3.2

Some $2$ e $5$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} (x^{7} + 1 x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.4

Multiplique $x^{5}$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} (x^{7} + x^{5}) + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.5

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} ((x^{2} + 1) x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.6

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} (x^{2} x^{3} + 1 x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.7

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

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Etapa 3.14.10.7.1

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

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} (x^{2 + 3} + 1 x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.7.2

Some $2$ e $3$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} (x^{5} + 1 x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.8

Multiplique $x^{3}$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} (x^{5} + x^{3}) + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.9

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} ((x^{2} + 1) x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.10

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} (x^{2} x + 1 x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.11

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

Toque para ver mais passagens...

Etapa 3.14.10.11.1

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

Toque para ver mais passagens...

Etapa 3.14.10.11.1.1

Eleve $x$ à potência de $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} (x^{2} x^{1} + 1 x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.11.1.2

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

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} (x^{2 + 1} + 1 x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.11.2

Some $2$ e $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} (x^{3} + 1 x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.12

Multiplique $x$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} (x^{3} + x) + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.13

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{2} + 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.14

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + (6 x^{2} + 6 \cdot 1) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.15

Multiplique $6$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + (6 x^{2} + 6) x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.16

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{2} x^{5} + 6 x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.17

Multiplique $x^{2}$ por $x^{5}$ somando os expoentes.

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Etapa 3.14.10.17.1

Mova $x^{5}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 (x^{5} x^{2}) + 6 x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.17.2

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

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{5 + 2} + 6 x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.17.3

Some $5$ e $2$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 (x^{2} + 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.18

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + (24 x^{2} + 24 \cdot 1) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.19

Multiplique $24$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + (24 x^{2} + 24) x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.20

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{2} x^{3} + 24 x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.21

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

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Etapa 3.14.10.21.1

Mova $x^{3}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 (x^{3} x^{2}) + 24 x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.21.2

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

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{3 + 2} + 24 x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.21.3

Some $3$ e $2$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 (x^{2} + 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.22

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + (24 x^{2} + 24 \cdot 1) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.23

Multiplique $24$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + (24 x^{2} + 24) x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.24

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{2} x + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.25

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

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Etapa 3.14.10.25.1

Mova $x$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 (x \cdot x^{2}) + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.25.2

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

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Etapa 3.14.10.25.2.1

Eleve $x$ à potência de $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 (x^{1} x^{2}) + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.25.2.2

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

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{1 + 2} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.25.3

Some $1$ e $2$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 (x^{2} + 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.26

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x + (- 7 x^{2} - 7 \cdot 1) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.27

Multiplique $- 7$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x + (- 7 x^{2} - 7) x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.28

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x + (- 7 x^{2} x^{6} - 7 x^{6}) e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.29

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

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Etapa 3.14.10.29.1

Mova $x^{6}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x + (- 7 (x^{6} x^{2}) - 7 x^{6}) e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.29.2

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

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x + (- 7 x^{6 + 2} - 7 x^{6}) e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.29.3

Some $6$ e $2$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x + (- 7 x^{8} - 7 x^{6}) e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.30

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 (x^{2} + 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.31

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} + (- 42 x^{2} - 42 \cdot 1) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.32

Multiplique $- 42$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} + (- 42 x^{2} - 42) x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.33

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} + (- 42 x^{2} x^{4} - 42 x^{4}) e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.34

Multiplique $x^{2}$ por $x^{4}$ somando os expoentes.

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Etapa 3.14.10.34.1

Mova $x^{4}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} + (- 42 (x^{4} x^{2}) - 42 x^{4}) e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.34.2

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

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} + (- 42 x^{4 + 2} - 42 x^{4}) e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.34.3

Some $4$ e $2$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} + (- 42 x^{6} - 42 x^{4}) e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.35

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 (x^{2} + 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.36

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} + (- 84 x^{2} - 84 \cdot 1) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.37

Multiplique $- 84$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} + (- 84 x^{2} - 84) x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.38

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} + (- 84 x^{2} x^{2} - 84 x^{2}) e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.39

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

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Etapa 3.14.10.39.1

Mova $x^{2}$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} + (- 84 (x^{2} x^{2}) - 84 x^{2}) e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.39.2

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

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} + (- 84 x^{2 + 2} - 84 x^{2}) e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.39.3

Some $2$ e $2$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} + (- 84 x^{4} - 84 x^{2}) e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.40

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 (x^{2} + 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.41

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} + (- 56 x^{2} - 56 \cdot 1) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.42

Multiplique $- 56$ por $1$ .

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} + (- 56 x^{2} - 56) e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.43

Aplique a propriedade distributiva.

$\frac{{(x^{2} + 1)}^{9} (6 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 20 e^{x} (x^{7}) + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.44

Some $6 e^{x} x^{7}$ e $20 e^{x} (x^{7})$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 6 e^{x} x^{5} + 24 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.45

Some $6 e^{x} x^{5}$ e $24 e^{x} x^{5}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 30 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 120 e^{x} (x^{5}) + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.46

Some $30 e^{x} x^{5}$ e $120 e^{x} (x^{5})$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 24 e^{x} x^{3} + 24 e^{x} x^{3} + 24 e^{x} x + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.47

Some $24 e^{x} x^{3}$ e $24 e^{x} x^{3}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 48 e^{x} x^{3} + 24 e^{x} x + 240 e^{x} (x^{3}) + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.48

Some $48 e^{x} x^{3}$ e $240 e^{x} (x^{3})$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 24 e^{x} x + 160 e^{x} (x) + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.49

Some $24 e^{x} x$ e $160 e^{x} (x)$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 6 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 20 x^{7} + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.50

Some $6 x^{7}$ e $20 x^{7}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 26 x^{7} + 6 x^{5} + 24 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.51

Some $6 x^{5}$ e $24 x^{5}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 26 x^{7} + 30 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 120 x^{5} + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.52

Some $30 x^{5}$ e $120 x^{5}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 26 x^{7} + 150 x^{5} + 24 x^{3} + 24 x^{3} + 24 x + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.53

Some $24 x^{3}$ e $24 x^{3}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 26 x^{7} + 150 x^{5} + 48 x^{3} + 24 x + 240 x^{3} + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.54

Some $48 x^{3}$ e $240 x^{3}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 26 x^{7} + 150 x^{5} + 288 x^{3} + 24 x + 160 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.55

Some $24 x$ e $160 x$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 26 x^{7} + 150 x^{5} + 288 x^{3} + 184 x - 7 x^{8} e^{x} - 7 x^{6} e^{x} - 42 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.56

Subtraia $42 x^{6} e^{x}$ de $- 7 x^{6} e^{x}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 26 x^{7} + 150 x^{5} + 288 x^{3} + 184 x - 7 x^{8} e^{x} - 49 x^{6} e^{x} - 42 x^{4} e^{x} - 84 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.57

Subtraia $84 x^{4} e^{x}$ de $- 42 x^{4} e^{x}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 26 x^{7} + 150 x^{5} + 288 x^{3} + 184 x - 7 x^{8} e^{x} - 49 x^{6} e^{x} - 126 x^{4} e^{x} - 84 x^{2} e^{x} - 56 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.58

Subtraia $56 x^{2} e^{x}$ de $- 84 x^{2} e^{x}$ .

$\frac{{(x^{2} + 1)}^{9} (26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x + 26 x^{7} + 150 x^{5} + 288 x^{3} + 184 x - 7 x^{8} e^{x} - 49 x^{6} e^{x} - 126 x^{4} e^{x} - 140 x^{2} e^{x} - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 3.14.10.59

Reordene os termos.

$\frac{{(x^{2} + 1)}^{9} (26 x^{7} + 150 x^{5} + 288 x^{3} + 26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x - 7 e^{x} x^{8} - 49 e^{x} x^{6} - 126 e^{x} x^{4} - 140 e^{x} x^{2} + 184 x - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 4

Reformule a equação definindo o lado esquerdo igual ao lado direito.

$y' = \frac{{(x^{2} + 1)}^{9} (26 x^{7} + 150 x^{5} + 288 x^{3} + 26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x - 7 e^{x} x^{8} - 49 e^{x} x^{6} - 126 e^{x} x^{4} - 140 e^{x} x^{2} + 184 x - 56 e^{x})}{{(e^{x} + 1)}^{8}}$

Etapa 5

Substitua $y'$ por $\frac{d y}{d x}$ .

$\frac{d y}{d x} = \frac{{(x^{2} + 1)}^{9} (26 x^{7} + 150 x^{5} + 288 x^{3} + 26 e^{x} x^{7} + 150 e^{x} x^{5} + 288 e^{x} x^{3} + 184 e^{x} x - 7 e^{x} x^{8} - 49 e^{x} x^{6} - 126 e^{x} x^{4} - 140 e^{x} x^{2} + 184 x - 56 e^{x})}{{(e^{x} + 1)}^{8}}$