Cálculo Exemplos

$y = \ln (\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{\sqrt{4 x + 1}})$

Etapa 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{4 x + 1}$ como ${(4 x + 1)}^{\frac{1}{2}}$ .

$y = \ln (\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}})$

Etapa 2

Diferencie os dois lados da equação.

$\frac{d}{d x} (y) = \frac{d}{d x} (\ln (\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}))$

Etapa 3

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

$y'$

Etapa 4

Diferencie o lado direito da equação.

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Etapa 4.1

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = \ln (x)$ e $g (x) = \frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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Etapa 4.1.1

Para aplicar a regra da cadeia, defina $u_{1}$ como $\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{d}{d u_{1}} [\ln (u_{1})] \frac{d}{d x} [\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}]$

Etapa 4.1.2

A derivada de $\ln (u_{1})$ em relação a $u_{1}$ é $\frac{1}{u_{1}}$ .

$\frac{1}{u_{1}} \frac{d}{d x} [\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}]$

Etapa 4.1.3

Substitua todas as ocorrências de $u_{1}$ por $\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{1}{\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}} \frac{d}{d x} [\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}]$

Etapa 4.2

Multiplique pelo inverso da fração para dividir por $\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

$1 \frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \frac{d}{d x} [\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}]$

Etapa 4.3

Multiplique $\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \frac{d}{d x} [\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}]$

Etapa 4.4

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 $f (x) = e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}$ e $g (x) = {(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} \frac{d}{d x} [e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}] - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{{({(4 x + 1)}^{\frac{1}{2}})}^{2}}$

Etapa 4.5

Multiplique os expoentes em ${({(4 x + 1)}^{\frac{1}{2}})}^{2}$ .

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Etapa 4.5.1

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

Etapa 4.5.2

Cancele o fator comum de $2$ .

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Etapa 4.5.2.1

Cancele o fator comum.

Etapa 4.5.2.2

Reescreva a expressão.

Etapa 4.6

Simplifique.

Etapa 4.7

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) \frac{d}{d x} [{(3 x + 1)}^{2}] + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.8

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{2}$ e $g (x) = 3 x + 1$ .

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Etapa 4.8.1

Para aplicar a regra da cadeia, defina $u_{2}$ como $3 x + 1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (\frac{d}{d u_{2}} [{u_{2}}^{2}] \frac{d}{d x} [3 x + 1]) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.8.2

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 $n = 2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (2 u_{2} \frac{d}{d x} [3 x + 1]) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.8.3

Substitua todas as ocorrências de $u_{2}$ por $3 x + 1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (2 (3 x + 1) \frac{d}{d x} [3 x + 1]) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.9

Diferencie.

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Etapa 4.9.1

De acordo com a regra da soma, a derivada de $3 x + 1$ com relação a $x$ é $\frac{d}{d x} [3 x] + \frac{d}{d x} [1]$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (2 (3 x + 1) (\frac{d}{d x} [3 x] + \frac{d}{d x} [1])) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.9.2

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (2 (3 x + 1) (3 \frac{d}{d x} [x] + \frac{d}{d x} [1])) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.9.3

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (2 (3 x + 1) (3 \cdot 1 + \frac{d}{d x} [1])) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.9.4

Multiplique $3$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (2 (3 x + 1) (3 + \frac{d}{d x} [1])) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.9.5

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (2 (3 x + 1) (3 + 0)) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.9.6

Simplifique a expressão.

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Etapa 4.9.6.1

Some $3$ e $0$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (2 (3 x + 1) \cdot 3) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.9.6.2

Multiplique $3$ por $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} \frac{d}{d x} [e^{x^{2}} (2 x + 1)]) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.10

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (e^{x^{2}} \frac{d}{d x} [2 x + 1] + (2 x + 1) \frac{d}{d x} [e^{x^{2}}])) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.11

Diferencie.

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Etapa 4.11.1

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (e^{x^{2}} (\frac{d}{d x} [2 x] + \frac{d}{d x} [1]) + (2 x + 1) \frac{d}{d x} [e^{x^{2}}])) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.11.2

Como $2$ é constante em relação a $x$ , a derivada de $2 x$ em relação a $x$ é $2 \frac{d}{d x} [x]$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (e^{x^{2}} (2 \frac{d}{d x} [x] + \frac{d}{d x} [1]) + (2 x + 1) \frac{d}{d x} [e^{x^{2}}])) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.11.3

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (e^{x^{2}} (2 \cdot 1 + \frac{d}{d x} [1]) + (2 x + 1) \frac{d}{d x} [e^{x^{2}}])) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.11.4

Multiplique $2$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (e^{x^{2}} (2 + \frac{d}{d x} [1]) + (2 x + 1) \frac{d}{d x} [e^{x^{2}}])) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.11.5

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (e^{x^{2}} (2 + 0) + (2 x + 1) \frac{d}{d x} [e^{x^{2}}])) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.11.6

Simplifique a expressão.

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Etapa 4.11.6.1

Some $2$ e $0$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (e^{x^{2}} \cdot 2 + (2 x + 1) \frac{d}{d x} [e^{x^{2}}])) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.11.6.2

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 \cdot e^{x^{2}} + (2 x + 1) \frac{d}{d x} [e^{x^{2}}])) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.12

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

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Etapa 4.12.1

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) (\frac{d}{d u_{3}} [e^{u_{3}}] \frac{d}{d x} [x^{2}]))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.12.2

Diferencie usando a regra exponencial, que determina que $\frac{d}{d u_{3}} [a^{u_{3}}]$ é $a^{u_{3}} \ln (a)$ , em que $a$ = $e$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) (e^{u_{3}} \frac{d}{d x} [x^{2}]))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.12.3

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) (e^{x^{2}} \frac{d}{d x} [x^{2}]))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.13

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [{(4 x + 1)}^{\frac{1}{2}}]}{4 x + 1}$

Etapa 4.14

Diferencie usando a regra da cadeia, que determina que $\frac{d}{d x} [f (g (x))]$ é $f' (g (x)) g' (x)$ , em que $f (x) = x^{\frac{1}{2}}$ e $g (x) = 4 x + 1$ .

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Etapa 4.14.1

Para aplicar a regra da cadeia, defina $u_{4}$ como $4 x + 1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{d}{d u_{4}} [{u_{4}}^{\frac{1}{2}}] \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.14.2

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{1}{2} {u_{4}}^{\frac{1}{2} - 1} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.14.3

Substitua todas as ocorrências de $u_{4}$ por $4 x + 1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{1}{2} {(4 x + 1)}^{\frac{1}{2} - 1} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.15

Para escrever $- 1$ como fração com um denominador comum, multiplique por $\frac{2}{2}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{1}{2} {(4 x + 1)}^{\frac{1}{2} - 1 \cdot \frac{2}{2}} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.16

Combine $- 1$ e $\frac{2}{2}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{1}{2} {(4 x + 1)}^{\frac{1}{2} + \frac{- 1 \cdot 2}{2}} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.17

Combine os numeradores em relação ao denominador comum.

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{1}{2} {(4 x + 1)}^{\frac{1 - 1 \cdot 2}{2}} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.18

Simplifique o numerador.

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Etapa 4.18.1

Multiplique $- 1$ por $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{1}{2} {(4 x + 1)}^{\frac{1 - 2}{2}} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.18.2

Subtraia $2$ de $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{1}{2} {(4 x + 1)}^{\frac{- 1}{2}} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.19

Combine frações.

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Etapa 4.19.1

Mova o número negativo para a frente da fração.

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{1}{2} {(4 x + 1)}^{- \frac{1}{2}} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.19.2

Combine $\frac{1}{2}$ e ${(4 x + 1)}^{- \frac{1}{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{{(4 x + 1)}^{- \frac{1}{2}}}{2} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.19.3

Mova ${(4 x + 1)}^{- \frac{1}{2}}$ para o denominador usando a regra do expoente negativo $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (\frac{1}{2 {(4 x + 1)}^{\frac{1}{2}}} \frac{d}{d x} [4 x + 1])}{4 x + 1}$

Etapa 4.19.4

Combine $\frac{1}{2 {(4 x + 1)}^{\frac{1}{2}}}$ e $e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1) {(3 x + 1)}^{2} \frac{d}{d x} [4 x + 1]}{4 x + 1}$

Etapa 4.19.5

Combine ${(3 x + 1)}^{2}$ e $\frac{e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{{(3 x + 1)}^{2} e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1) \frac{d}{d x} [4 x + 1]}{4 x + 1}$

Etapa 4.20

De acordo com a regra da soma, a derivada de $4 x + 1$ com relação a $x$ é $\frac{d}{d x} [4 x] + \frac{d}{d x} [1]$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{{(3 x + 1)}^{2} e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1) (\frac{d}{d x} [4 x] + \frac{d}{d x} [1])}{4 x + 1}$

Etapa 4.21

Como $4$ é constante em relação a $x$ , a derivada de $4 x$ em relação a $x$ é $4 \frac{d}{d x} [x]$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{{(3 x + 1)}^{2} e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1) (4 \frac{d}{d x} [x] + \frac{d}{d x} [1])}{4 x + 1}$

Etapa 4.22

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{{(3 x + 1)}^{2} e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1) (4 \cdot 1 + \frac{d}{d x} [1])}{4 x + 1}$

Etapa 4.23

Multiplique $4$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{{(3 x + 1)}^{2} e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1) (4 + \frac{d}{d x} [1])}{4 x + 1}$

Etapa 4.24

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

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{{(3 x + 1)}^{2} e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1) (4 + 0)}{4 x + 1}$

Etapa 4.25

Simplifique os termos.

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Etapa 4.25.1

Some $4$ e $0$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{{(3 x + 1)}^{2} e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1) \cdot 4}{4 x + 1}$

Etapa 4.25.2

Multiplique $4$ por $- 1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - 4 \frac{{(3 x + 1)}^{2} e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{4 x + 1}$

Etapa 4.25.3

Combine $- 4$ e $\frac{{(3 x + 1)}^{2} e^{x^{2}}}{2 {(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) + \frac{- 4 ({(3 x + 1)}^{2} e^{x^{2}})}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{4 x + 1}$

Etapa 4.25.4

Fatore $2$ de $- 4 {(3 x + 1)}^{2} e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) + \frac{2 (- 2 {(3 x + 1)}^{2} e^{x^{2}})}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{4 x + 1}$

Etapa 4.26

Cancele os fatores comuns.

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Etapa 4.26.1

Fatore $2$ de $2 {(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) + \frac{2 (- 2 {(3 x + 1)}^{2} e^{x^{2}})}{2 ({(4 x + 1)}^{\frac{1}{2}})} (2 x + 1)}{4 x + 1}$

Etapa 4.26.2

Cancele o fator comum.

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) + \frac{2 (- 2 {(3 x + 1)}^{2} e^{x^{2}})}{2 {(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{4 x + 1}$

Etapa 4.26.3

Reescreva a expressão.

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) + \frac{- 2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{4 x + 1}$

Etapa 4.27

Mova o número negativo para a frente da fração.

$\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}} \cdot \frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{4 x + 1}$

Etapa 4.28

Multiplique $\frac{{(4 x + 1)}^{\frac{1}{2}}}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}$ por $\frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{4 x + 1}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} ({(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1))}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (4 x + 1)}$

Etapa 4.29

Mova ${(4 x + 1)}^{\frac{1}{2}}$ para o denominador usando a regra do expoente negativo $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (e^{x^{2}} (2 x + 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} (4 x + 1) {(4 x + 1)}^{- \frac{1}{2}}}$

Etapa 4.30

Multiplique $4 x + 1$ por ${(4 x + 1)}^{- \frac{1}{2}}$ somando os expoentes.

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Etapa 4.30.1

Mova ${(4 x + 1)}^{- \frac{1}{2}}$ .

Etapa 4.30.2

Multiplique ${(4 x + 1)}^{- \frac{1}{2}}$ por $4 x + 1$ .

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Etapa 4.30.2.1

Eleve $4 x + 1$ à potência de $1$ .

Etapa 4.30.2.2

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

Etapa 4.30.3

Escreva $1$ como uma fração com um denominador comum.

Etapa 4.30.4

Combine os numeradores em relação ao denominador comum.

Etapa 4.30.5

Some $- 1$ e $2$ .

Etapa 4.31

Simplifique.

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Etapa 4.31.1

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) (6 (3 x + 1)) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.2

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) (6 (3 x) + 6 \cdot 1) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x + 1) e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.3

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) (6 (3 x) + 6 \cdot 1) + {(3 x + 1)}^{2} (2 e^{x^{2}} + (2 x e^{x^{2}} + 1 e^{x^{2}}) (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.4

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) (6 (3 x) + 6 \cdot 1) + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.5

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) (6 (3 x) + 6 \cdot 1) + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6

Simplifique o numerador.

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Etapa 4.31.6.1

Simplifique cada termo.

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Etapa 4.31.6.1.1

Simplifique cada termo.

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Etapa 4.31.6.1.1.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} ((2 e^{x^{2}} x + e^{x^{2}} \cdot 1) (6 (3 x) + 6 \cdot 1) + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.1.2

Multiplique $e^{x^{2}}$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} ((2 e^{x^{2}} x + e^{x^{2}}) (6 (3 x) + 6 \cdot 1) + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.2

Simplifique cada termo.

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Etapa 4.31.6.1.2.1

Multiplique $3$ por $6$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} ((2 e^{x^{2}} x + e^{x^{2}}) (18 x + 6 \cdot 1) + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.2.2

Multiplique $6$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} ((2 e^{x^{2}} x + e^{x^{2}}) (18 x + 6) + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.3

Expanda $(2 e^{x^{2}} x + e^{x^{2}}) (18 x + 6)$ usando o método FOIL.

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Etapa 4.31.6.1.3.1

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (2 e^{x^{2}} x (18 x + 6) + e^{x^{2}} (18 x + 6) + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.3.2

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (2 e^{x^{2}} x (18 x) + 2 e^{x^{2}} x \cdot 6 + e^{x^{2}} (18 x + 6) + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.3.3

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (2 e^{x^{2}} x (18 x) + 2 e^{x^{2}} x \cdot 6 + e^{x^{2}} (18 x) + e^{x^{2}} \cdot 6 + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.4

Simplifique e combine termos semelhantes.

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Etapa 4.31.6.1.4.1

Simplifique cada termo.

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Etapa 4.31.6.1.4.1.1

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 4.31.6.1.4.1.1.1

Mova $x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (2 e^{x^{2}} (x \cdot x) \cdot 18 + 2 e^{x^{2}} x \cdot 6 + e^{x^{2}} (18 x) + e^{x^{2}} \cdot 6 + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.4.1.1.2

Multiplique $x$ por $x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (2 e^{x^{2}} x^{2} \cdot 18 + 2 e^{x^{2}} x \cdot 6 + e^{x^{2}} (18 x) + e^{x^{2}} \cdot 6 + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.4.1.2

Multiplique $18$ por $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 2 e^{x^{2}} x \cdot 6 + e^{x^{2}} (18 x) + e^{x^{2}} \cdot 6 + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.4.1.3

Multiplique $6$ por $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 12 e^{x^{2}} x + e^{x^{2}} (18 x) + e^{x^{2}} \cdot 6 + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.4.1.4

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 12 e^{x^{2}} x + 18 e^{x^{2}} x + e^{x^{2}} \cdot 6 + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.4.1.5

Mova $6$ para a esquerda de $e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 12 e^{x^{2}} x + 18 e^{x^{2}} x + 6 e^{x^{2}} + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.4.2

Some $12 e^{x^{2}} x$ e $18 e^{x^{2}} x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + {(3 x + 1)}^{2} (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.5

Reescreva ${(3 x + 1)}^{2}$ como $(3 x + 1) (3 x + 1)$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (3 x + 1) (3 x + 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.6

Expanda $(3 x + 1) (3 x + 1)$ usando o método FOIL.

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Etapa 4.31.6.1.6.1

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (3 x (3 x + 1) + 1 (3 x + 1)) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.6.2

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (3 x (3 x) + 3 x \cdot 1 + 1 (3 x + 1)) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.6.3

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (3 x (3 x) + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.7

Simplifique e combine termos semelhantes.

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Etapa 4.31.6.1.7.1

Simplifique cada termo.

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Etapa 4.31.6.1.7.1.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (3 \cdot 3 x \cdot x + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.7.1.2

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 4.31.6.1.7.1.2.1

Mova $x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (3 \cdot 3 (x \cdot x) + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.7.1.2.2

Multiplique $x$ por $x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (3 \cdot 3 x^{2} + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.7.1.3

Multiplique $3$ por $3$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.7.1.4

Multiplique $3$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 3 x + 1 (3 x) + 1 \cdot 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.7.1.5

Multiplique $3 x$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 3 x + 3 x + 1 \cdot 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.7.1.6

Multiplique $1$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 3 x + 3 x + 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.7.2

Some $3 x$ e $3 x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 6 x + 1) (2 e^{x^{2}} + 2 x e^{x^{2}} (2 x) + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.8

Simplifique cada termo.

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Etapa 4.31.6.1.8.1

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 4.31.6.1.8.1.1

Mova $x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 6 x + 1) (2 e^{x^{2}} + 2 (x \cdot x) e^{x^{2}} \cdot 2 + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.8.1.2

Multiplique $x$ por $x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 6 x + 1) (2 e^{x^{2}} + 2 x^{2} e^{x^{2}} \cdot 2 + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.8.2

Multiplique $2$ por $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 6 x + 1) (2 e^{x^{2}} + 4 x^{2} e^{x^{2}} + 1 e^{x^{2}} (2 x))) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.8.3

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 6 x + 1) (2 e^{x^{2}} + 4 x^{2} e^{x^{2}} + 1 \cdot 2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.8.4

Multiplique $2$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + (9 x^{2} + 6 x + 1) (2 e^{x^{2}} + 4 x^{2} e^{x^{2}} + 2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.9

Expanda $(9 x^{2} + 6 x + 1) (2 e^{x^{2}} + 4 x^{2} e^{x^{2}} + 2 e^{x^{2}} x)$ multiplicando cada termo na primeira expressão por cada um dos termos na segunda expressão.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 9 x^{2} (2 e^{x^{2}}) + 9 x^{2} (4 x^{2} e^{x^{2}}) + 9 x^{2} (2 e^{x^{2}} x) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10

Simplifique cada termo.

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Etapa 4.31.6.1.10.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 9 \cdot 2 x^{2} e^{x^{2}} + 9 x^{2} (4 x^{2} e^{x^{2}}) + 9 x^{2} (2 e^{x^{2}} x) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.2

Multiplique $9$ por $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 9 x^{2} (4 x^{2} e^{x^{2}}) + 9 x^{2} (2 e^{x^{2}} x) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.3

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

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Etapa 4.31.6.1.10.3.1

Mova $x^{2}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 9 (x^{2} x^{2}) (4 e^{x^{2}}) + 9 x^{2} (2 e^{x^{2}} x) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.3.2

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

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 9 x^{2 + 2} (4 e^{x^{2}}) + 9 x^{2} (2 e^{x^{2}} x) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.3.3

Some $2$ e $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 9 x^{4} (4 e^{x^{2}}) + 9 x^{2} (2 e^{x^{2}} x) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.4

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 9 \cdot 4 x^{4} e^{x^{2}} + 9 x^{2} (2 e^{x^{2}} x) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.5

Multiplique $9$ por $4$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 9 x^{2} (2 e^{x^{2}} x) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.6

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

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Etapa 4.31.6.1.10.6.1

Mova $x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 9 (x \cdot x^{2}) (2 e^{x^{2}}) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.6.2

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

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Etapa 4.31.6.1.10.6.2.1

Eleve $x$ à potência de $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 9 (x^{1} x^{2}) (2 e^{x^{2}}) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.6.2.2

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

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 9 x^{1 + 2} (2 e^{x^{2}}) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.6.3

Some $1$ e $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 9 x^{3} (2 e^{x^{2}}) + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.7

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 9 \cdot 2 x^{3} e^{x^{2}} + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.8

Multiplique $9$ por $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 6 x (2 e^{x^{2}}) + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.9

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 6 \cdot 2 x e^{x^{2}} + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.10

Multiplique $6$ por $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 6 x (4 x^{2} e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.11

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

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Etapa 4.31.6.1.10.11.1

Mova $x^{2}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 6 (x^{2} x) (4 e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.11.2

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

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Etapa 4.31.6.1.10.11.2.1

Eleve $x$ à potência de $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 6 (x^{2} x^{1}) (4 e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.11.2.2

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

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 6 x^{2 + 1} (4 e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.11.3

Some $2$ e $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 6 x^{3} (4 e^{x^{2}}) + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.12

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 6 \cdot 4 x^{3} e^{x^{2}} + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.13

Multiplique $6$ por $4$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 6 x (2 e^{x^{2}} x) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.14

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 4.31.6.1.10.14.1

Mova $x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 6 (x \cdot x) (2 e^{x^{2}}) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.14.2

Multiplique $x$ por $x$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 6 x^{2} (2 e^{x^{2}}) + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.15

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 6 \cdot 2 x^{2} e^{x^{2}} + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.16

Multiplique $6$ por $2$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 12 x^{2} e^{x^{2}} + 1 (2 e^{x^{2}}) + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.17

Multiplique $2 e^{x^{2}}$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 12 x^{2} e^{x^{2}} + 2 e^{x^{2}} + 1 (4 x^{2} e^{x^{2}}) + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.18

Multiplique $4 x^{2} e^{x^{2}}$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 12 x^{2} e^{x^{2}} + 2 e^{x^{2}} + 4 x^{2} e^{x^{2}} + 1 (2 e^{x^{2}} x)) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.10.19

Multiplique $2 e^{x^{2}} x$ por $1$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 18 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 12 x^{2} e^{x^{2}} + 2 e^{x^{2}} + 4 x^{2} e^{x^{2}} + 2 e^{x^{2}} x) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.11

Some $18 x^{2} e^{x^{2}}$ e $12 x^{2} e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 30 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 2 e^{x^{2}} + 4 x^{2} e^{x^{2}} + 2 e^{x^{2}} x) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.12

Some $30 x^{2} e^{x^{2}}$ e $4 x^{2} e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 34 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 18 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 24 x^{3} e^{x^{2}} + 2 e^{x^{2}} + 2 e^{x^{2}} x) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.13

Some $18 x^{3} e^{x^{2}}$ e $24 x^{3} e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 34 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 42 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 2 e^{x^{2}} + 2 e^{x^{2}} x) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.14

Some $12 x e^{x^{2}}$ e $2 e^{x^{2}} x$ .

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Etapa 4.31.6.1.14.1

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

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 34 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 42 x^{3} e^{x^{2}} + 12 x e^{x^{2}} + 2 x e^{x^{2}} + 2 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.1.14.2

Some $12 x e^{x^{2}}$ e $2 x e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 e^{x^{2}} x^{2} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 34 x^{2} e^{x^{2}} + 36 x^{4} e^{x^{2}} + 42 x^{3} e^{x^{2}} + 14 x e^{x^{2}} + 2 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.2

Some $36 e^{x^{2}} x^{2}$ e $34 x^{2} e^{x^{2}}$ .

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Etapa 4.31.6.2.1

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

$\frac{{(4 x + 1)}^{\frac{1}{2}} (36 x^{2} e^{x^{2}} + 34 x^{2} e^{x^{2}} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 36 x^{4} e^{x^{2}} + 42 x^{3} e^{x^{2}} + 14 x e^{x^{2}} + 2 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.2.2

Some $36 x^{2} e^{x^{2}}$ e $34 x^{2} e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (70 x^{2} e^{x^{2}} + 30 e^{x^{2}} x + 6 e^{x^{2}} + 36 x^{4} e^{x^{2}} + 42 x^{3} e^{x^{2}} + 14 x e^{x^{2}} + 2 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.3

Some $30 e^{x^{2}} x$ e $14 x e^{x^{2}}$ .

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Etapa 4.31.6.3.1

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

$\frac{{(4 x + 1)}^{\frac{1}{2}} (70 x^{2} e^{x^{2}} + 30 x e^{x^{2}} + 14 x e^{x^{2}} + 6 e^{x^{2}} + 36 x^{4} e^{x^{2}} + 42 x^{3} e^{x^{2}} + 2 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.3.2

Some $30 x e^{x^{2}}$ e $14 x e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (70 x^{2} e^{x^{2}} + 44 x e^{x^{2}} + 6 e^{x^{2}} + 36 x^{4} e^{x^{2}} + 42 x^{3} e^{x^{2}} + 2 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.4

Some $6 e^{x^{2}}$ e $2 e^{x^{2}}$ .

$\frac{{(4 x + 1)}^{\frac{1}{2}} (70 x^{2} e^{x^{2}} + 44 x e^{x^{2}} + 36 x^{4} e^{x^{2}} + 42 x^{3} e^{x^{2}} + 8 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.5

Aplique a propriedade distributiva.

$\frac{{(4 x + 1)}^{\frac{1}{2}} (70 x^{2} e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (44 x e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (36 x^{4} e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (42 x^{3} e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (8 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.6

Simplifique.

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Etapa 4.31.6.6.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + {(4 x + 1)}^{\frac{1}{2}} (44 x e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (36 x^{4} e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (42 x^{3} e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (8 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.6.2

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + {(4 x + 1)}^{\frac{1}{2}} (36 x^{4} e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (42 x^{3} e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (8 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.6.3

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + {(4 x + 1)}^{\frac{1}{2}} (42 x^{3} e^{x^{2}}) + {(4 x + 1)}^{\frac{1}{2}} (8 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.6.4

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + {(4 x + 1)}^{\frac{1}{2}} (8 e^{x^{2}}) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.6.5

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x + 1)}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.7

Aplique a propriedade distributiva.

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x) - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} \cdot 1}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.8

Multiplique $- \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} (2 x)$ .

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Etapa 4.31.6.8.1

Multiplique $2$ por $- 1$ .

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} - 2 \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} x - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} \cdot 1}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.8.2

Combine $- 2$ e $\frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{- 2 (2 {(3 x + 1)}^{2} e^{x^{2}})}{{(4 x + 1)}^{\frac{1}{2}}} x - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} \cdot 1}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.8.3

Multiplique $2$ por $- 2$ .

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{- 4 ({(3 x + 1)}^{2} e^{x^{2}})}{{(4 x + 1)}^{\frac{1}{2}}} x - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} \cdot 1}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.8.4

Combine $\frac{- 4 ({(3 x + 1)}^{2} e^{x^{2}})}{{(4 x + 1)}^{\frac{1}{2}}}$ e $x$ .

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{- 4 ({(3 x + 1)}^{2} e^{x^{2}}) x}{{(4 x + 1)}^{\frac{1}{2}}} - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}} \cdot 1}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.9

Multiplique $- 1$ por $1$ .

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{- 4 ({(3 x + 1)}^{2} e^{x^{2}}) x}{{(4 x + 1)}^{\frac{1}{2}}} - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.10

Mova o número negativo para a frente da fração.

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} - \frac{4 {(3 x + 1)}^{2} e^{x^{2}} x}{{(4 x + 1)}^{\frac{1}{2}}} - \frac{2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.11

Combine os numeradores em relação ao denominador comum.

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{- 4 {(3 x + 1)}^{2} e^{x^{2}} x - 2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.12

Fatore $2 {(3 x + 1)}^{2} e^{x^{2}}$ de $- 4 {(3 x + 1)}^{2} e^{x^{2}} x - 2 {(3 x + 1)}^{2} e^{x^{2}}$ .

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Etapa 4.31.6.12.1

Fatore $2 {(3 x + 1)}^{2} e^{x^{2}}$ de $- 4 {(3 x + 1)}^{2} e^{x^{2}} x$ .

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{2 {(3 x + 1)}^{2} e^{x^{2}} (- 2 x) - 2 {(3 x + 1)}^{2} e^{x^{2}}}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.12.2

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

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{2 {(3 x + 1)}^{2} e^{x^{2}} (- 2 x) + 2 {(3 x + 1)}^{2} e^{x^{2}} (- 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.12.3

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

$\frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} + 44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{2 {(3 x + 1)}^{2} e^{x^{2}} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.13

Para escrever $70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}}$ como fração com um denominador comum, multiplique por $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}} + \frac{2 {(3 x + 1)}^{2} e^{x^{2}} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.14

Combine os numeradores em relação ao denominador comum.

$\frac{44 {(4 x + 1)}^{\frac{1}{2}} x e^{x^{2}} + 36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + \frac{70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 {(3 x + 1)}^{2} e^{x^{2}} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.15

Mova ${(3 x + 1)}^{2}$ .

$\frac{36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}} + 42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + 44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.16

Some $36 {(4 x + 1)}^{\frac{1}{2}} x^{4} e^{x^{2}}$ e $\frac{70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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Etapa 4.31.6.16.1

Mova ${(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + 44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.16.2

Para escrever $36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}}$ como fração com um denominador comum, multiplique por $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + 44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}} + \frac{70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.16.3

Combine os numeradores em relação ao denominador comum.

$\frac{42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}} + 8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + 44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.17

Some $42 {(4 x + 1)}^{\frac{1}{2}} x^{3} e^{x^{2}}$ e $\frac{36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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Etapa 4.31.6.17.1

Mova ${(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + 44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + 42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.17.2

Para escrever $42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}}$ como fração com um denominador comum, multiplique por $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + 44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}} + \frac{36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.17.3

Combine os numeradores em relação ao denominador comum.

$\frac{8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}} + 44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.18

Some $8 {(4 x + 1)}^{\frac{1}{2}} e^{x^{2}}$ e $\frac{42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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Etapa 4.31.6.18.1

Mova ${(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + 8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.18.2

Para escrever $8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}}$ como fração com um denominador comum, multiplique por $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}} + \frac{42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.18.3

Combine os numeradores em relação ao denominador comum.

$\frac{44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} + \frac{8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.19

Para escrever $44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}}$ como fração com um denominador comum, multiplique por $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{\frac{44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}} + \frac{8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.20

Combine os numeradores em relação ao denominador comum.

$\frac{\frac{44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 x^{2} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.21

Reordene os termos.

$\frac{\frac{44 e^{x^{2}} x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 42 e^{x^{2}} x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 e^{x^{2}} x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22

Reescreva $\frac{44 e^{x^{2}} x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 42 e^{x^{2}} x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 e^{x^{2}} x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}$ em uma forma fatorada.

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Etapa 4.31.6.22.1

Fatore $2 e^{x^{2}}$ de $44 e^{x^{2}} x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 42 e^{x^{2}} x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 e^{x^{2}} x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)$ .

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Etapa 4.31.6.22.1.1

Fatore $2 e^{x^{2}}$ de $44 e^{x^{2}} x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 42 e^{x^{2}} x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 e^{x^{2}} x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.2

Fatore $2 e^{x^{2}}$ de $8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 42 e^{x^{2}} x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 e^{x^{2}} x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.3

Fatore $2 e^{x^{2}}$ de $42 e^{x^{2}} x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 36 e^{x^{2}} x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.4

Fatore $2 e^{x^{2}}$ de $36 e^{x^{2}} x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.5

Fatore $2 e^{x^{2}}$ de $70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.6

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

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} ({(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.7

Fatore $2 e^{x^{2}}$ de $2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}})$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} ({(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.8

Fatore $2 e^{x^{2}}$ de $2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}})$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} ({(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.9

Fatore $2 e^{x^{2}}$ de $2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}})$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} ({(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.10

Fatore $2 e^{x^{2}}$ de $2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}})$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} ({(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.1.11

Fatore $2 e^{x^{2}}$ de $2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} ({(3 x + 1)}^{2} (- 2 x - 1))$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2

Combine expoentes.

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Etapa 4.31.6.22.2.1

Multiplique ${(4 x + 1)}^{\frac{1}{2}}$ por ${(4 x + 1)}^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.31.6.22.2.1.1

Mova ${(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x ({(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.1.2

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

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2} + \frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.1.3

Combine os numeradores em relação ao denominador comum.

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1 + 1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.1.4

Some $1$ e $1$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{2}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.1.5

Divida $2$ por $2$ .

$\frac{\frac{2 e^{x^{2}} (22 x {(4 x + 1)}^{1} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.2

Simplifique $22 x {(4 x + 1)}^{1}$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.3

Multiplique ${(4 x + 1)}^{\frac{1}{2}}$ por ${(4 x + 1)}^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.31.6.22.2.3.1

Mova ${(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 ({(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.3.2

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

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 {(4 x + 1)}^{\frac{1}{2} + \frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.3.3

Combine os numeradores em relação ao denominador comum.

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 {(4 x + 1)}^{\frac{1 + 1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.3.4

Some $1$ e $1$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 {(4 x + 1)}^{\frac{2}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.3.5

Divida $2$ por $2$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 {(4 x + 1)}^{1} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.4

Simplifique $4 {(4 x + 1)}^{1}$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.5

Multiplique ${(4 x + 1)}^{\frac{1}{2}}$ por ${(4 x + 1)}^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.31.6.22.2.5.1

Mova ${(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} ({(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.5.2

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

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} {(4 x + 1)}^{\frac{1}{2} + \frac{1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.5.3

Combine os numeradores em relação ao denominador comum.

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} {(4 x + 1)}^{\frac{1 + 1}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.5.4

Some $1$ e $1$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} {(4 x + 1)}^{\frac{2}{2}} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.5.5

Divida $2$ por $2$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} {(4 x + 1)}^{1} + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.6

Simplifique $21 x^{3} {(4 x + 1)}^{1}$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.7

Multiplique ${(4 x + 1)}^{\frac{1}{2}}$ por ${(4 x + 1)}^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.31.6.22.2.7.1

Mova ${(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} ({(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.7.2

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

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} {(4 x + 1)}^{\frac{1}{2} + \frac{1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.7.3

Combine os numeradores em relação ao denominador comum.

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} {(4 x + 1)}^{\frac{1 + 1}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.7.4

Some $1$ e $1$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} {(4 x + 1)}^{\frac{2}{2}} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.7.5

Divida $2$ por $2$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} {(4 x + 1)}^{1} + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.8

Simplifique $18 x^{4} {(4 x + 1)}^{1}$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.9

Multiplique ${(4 x + 1)}^{\frac{1}{2}}$ por ${(4 x + 1)}^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.31.6.22.2.9.1

Mova ${(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} ({(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.9.2

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

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} {(4 x + 1)}^{\frac{1}{2} + \frac{1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.9.3

Combine os numeradores em relação ao denominador comum.

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} {(4 x + 1)}^{\frac{1 + 1}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.9.4

Some $1$ e $1$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} {(4 x + 1)}^{\frac{2}{2}} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.9.5

Divida $2$ por $2$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} {(4 x + 1)}^{1} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.22.2.10

Simplifique $35 x^{2} {(4 x + 1)}^{1}$ .

$\frac{\frac{2 e^{x^{2}} (22 x (4 x + 1) + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23

Simplifique o numerador.

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Etapa 4.31.6.23.1

Aplique a propriedade distributiva.

$\frac{\frac{2 e^{x^{2}} (22 x (4 x) + 22 x \cdot 1 + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.2

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{\frac{2 e^{x^{2}} (22 \cdot 4 x \cdot x + 22 x \cdot 1 + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.3

Multiplique $22$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (22 \cdot 4 x \cdot x + 22 x + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.4

Simplifique cada termo.

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Etapa 4.31.6.23.4.1

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 4.31.6.23.4.1.1

Mova $x$ .

$\frac{\frac{2 e^{x^{2}} (22 \cdot 4 (x \cdot x) + 22 x + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.4.1.2

Multiplique $x$ por $x$ .

$\frac{\frac{2 e^{x^{2}} (22 \cdot 4 x^{2} + 22 x + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.4.2

Multiplique $22$ por $4$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 4 (4 x + 1) + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.5

Aplique a propriedade distributiva.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 4 (4 x) + 4 \cdot 1 + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.6

Multiplique $4$ por $4$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 \cdot 1 + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.7

Multiplique $4$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 21 x^{3} (4 x + 1) + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.8

Aplique a propriedade distributiva.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 21 x^{3} (4 x) + 21 x^{3} \cdot 1 + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.9

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 21 \cdot 4 x^{3} x + 21 x^{3} \cdot 1 + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.10

Multiplique $21$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 21 \cdot 4 x^{3} x + 21 x^{3} + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.11

Simplifique cada termo.

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Etapa 4.31.6.23.11.1

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

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Etapa 4.31.6.23.11.1.1

Mova $x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 21 \cdot 4 (x \cdot x^{3}) + 21 x^{3} + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.11.1.2

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

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Etapa 4.31.6.23.11.1.2.1

Eleve $x$ à potência de $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 21 \cdot 4 (x^{1} x^{3}) + 21 x^{3} + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.11.1.2.2

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

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 21 \cdot 4 x^{1 + 3} + 21 x^{3} + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.11.1.3

Some $1$ e $3$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 21 \cdot 4 x^{4} + 21 x^{3} + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.11.2

Multiplique $21$ por $4$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 18 x^{4} (4 x + 1) + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.12

Aplique a propriedade distributiva.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 18 x^{4} (4 x) + 18 x^{4} \cdot 1 + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.13

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 18 \cdot 4 x^{4} x + 18 x^{4} \cdot 1 + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.14

Multiplique $18$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 18 \cdot 4 x^{4} x + 18 x^{4} + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.15

Simplifique cada termo.

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Etapa 4.31.6.23.15.1

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

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Etapa 4.31.6.23.15.1.1

Mova $x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 18 \cdot 4 (x \cdot x^{4}) + 18 x^{4} + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.15.1.2

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

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Etapa 4.31.6.23.15.1.2.1

Eleve $x$ à potência de $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 18 \cdot 4 (x^{1} x^{4}) + 18 x^{4} + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.15.1.2.2

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

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 18 \cdot 4 x^{1 + 4} + 18 x^{4} + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.15.1.3

Some $1$ e $4$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 18 \cdot 4 x^{5} + 18 x^{4} + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.15.2

Multiplique $18$ por $4$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 35 x^{2} (4 x + 1) + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.16

Aplique a propriedade distributiva.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 35 x^{2} (4 x) + 35 x^{2} \cdot 1 + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.17

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 35 \cdot 4 x^{2} x + 35 x^{2} \cdot 1 + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.18

Multiplique $35$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 35 \cdot 4 x^{2} x + 35 x^{2} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.19

Simplifique cada termo.

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Etapa 4.31.6.23.19.1

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

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Etapa 4.31.6.23.19.1.1

Mova $x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 35 \cdot 4 (x \cdot x^{2}) + 35 x^{2} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.19.1.2

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

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Etapa 4.31.6.23.19.1.2.1

Eleve $x$ à potência de $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 35 \cdot 4 (x^{1} x^{2}) + 35 x^{2} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.19.1.2.2

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

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 35 \cdot 4 x^{1 + 2} + 35 x^{2} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.19.1.3

Some $1$ e $2$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 35 \cdot 4 x^{3} + 35 x^{2} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.19.2

Multiplique $35$ por $4$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + {(3 x + 1)}^{2} (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.20

Reescreva ${(3 x + 1)}^{2}$ como $(3 x + 1) (3 x + 1)$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (3 x + 1) (3 x + 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.21

Expanda $(3 x + 1) (3 x + 1)$ usando o método FOIL.

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Etapa 4.31.6.23.21.1

Aplique a propriedade distributiva.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (3 x (3 x + 1) + 1 (3 x + 1)) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.21.2

Aplique a propriedade distributiva.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (3 x (3 x) + 3 x \cdot 1 + 1 (3 x + 1)) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.21.3

Aplique a propriedade distributiva.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (3 x (3 x) + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.22

Simplifique e combine termos semelhantes.

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Etapa 4.31.6.23.22.1

Simplifique cada termo.

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Etapa 4.31.6.23.22.1.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (3 \cdot 3 x \cdot x + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.22.1.2

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 4.31.6.23.22.1.2.1

Mova $x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (3 \cdot 3 (x \cdot x) + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.22.1.2.2

Multiplique $x$ por $x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (3 \cdot 3 x^{2} + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.22.1.3

Multiplique $3$ por $3$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (9 x^{2} + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.22.1.4

Multiplique $3$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (9 x^{2} + 3 x + 1 (3 x) + 1 \cdot 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.22.1.5

Multiplique $3 x$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (9 x^{2} + 3 x + 3 x + 1 \cdot 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.22.1.6

Multiplique $1$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (9 x^{2} + 3 x + 3 x + 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.22.2

Some $3 x$ e $3 x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + (9 x^{2} + 6 x + 1) (- 2 x - 1))}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.23

Expanda $(9 x^{2} + 6 x + 1) (- 2 x - 1)$ multiplicando cada termo na primeira expressão por cada um dos termos na segunda expressão.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + 9 x^{2} (- 2 x) + 9 x^{2} \cdot - 1 + 6 x (- 2 x) + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24

Simplifique cada termo.

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Etapa 4.31.6.23.24.1

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + 9 \cdot - 2 x^{2} x + 9 x^{2} \cdot - 1 + 6 x (- 2 x) + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.2

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

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Etapa 4.31.6.23.24.2.1

Mova $x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + 9 \cdot - 2 (x \cdot x^{2}) + 9 x^{2} \cdot - 1 + 6 x (- 2 x) + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.2.2

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

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Etapa 4.31.6.23.24.2.2.1

Eleve $x$ à potência de $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + 9 \cdot - 2 (x^{1} x^{2}) + 9 x^{2} \cdot - 1 + 6 x (- 2 x) + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.2.2.2

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

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + 9 \cdot - 2 x^{1 + 2} + 9 x^{2} \cdot - 1 + 6 x (- 2 x) + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.2.3

Some $1$ e $2$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} + 9 \cdot - 2 x^{3} + 9 x^{2} \cdot - 1 + 6 x (- 2 x) + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.3

Multiplique $9$ por $- 2$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} + 9 x^{2} \cdot - 1 + 6 x (- 2 x) + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.4

Multiplique $- 1$ por $9$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 9 x^{2} + 6 x (- 2 x) + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.5

Reescreva usando a propriedade comutativa da multiplicação.

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 9 x^{2} + 6 \cdot - 2 x \cdot x + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.6

Multiplique $x$ por $x$ somando os expoentes.

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Etapa 4.31.6.23.24.6.1

Mova $x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 9 x^{2} + 6 \cdot - 2 (x \cdot x) + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.6.2

Multiplique $x$ por $x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 9 x^{2} + 6 \cdot - 2 x^{2} + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.7

Multiplique $6$ por $- 2$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 9 x^{2} - 12 x^{2} + 6 x \cdot - 1 + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.8

Multiplique $- 1$ por $6$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 9 x^{2} - 12 x^{2} - 6 x + 1 (- 2 x) + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.9

Multiplique $- 2 x$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 9 x^{2} - 12 x^{2} - 6 x - 2 x + 1 \cdot - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.24.10

Multiplique $- 1$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 9 x^{2} - 12 x^{2} - 6 x - 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.25

Subtraia $12 x^{2}$ de $- 9 x^{2}$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 21 x^{2} - 6 x - 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.26

Subtraia $2 x$ de $- 6 x$ .

$\frac{\frac{2 e^{x^{2}} (88 x^{2} + 22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 35 x^{2} - 18 x^{3} - 21 x^{2} - 8 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.27

Some $88 x^{2}$ e $35 x^{2}$ .

$\frac{\frac{2 e^{x^{2}} (22 x + 16 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 123 x^{2} - 18 x^{3} - 21 x^{2} - 8 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.28

Some $22 x$ e $16 x$ .

$\frac{\frac{2 e^{x^{2}} (38 x + 4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 123 x^{2} - 18 x^{3} - 21 x^{2} - 8 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.29

Subtraia $8 x$ de $38 x$ .

$\frac{\frac{2 e^{x^{2}} (4 + 84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 123 x^{2} - 18 x^{3} - 21 x^{2} + 30 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.30

Subtraia $1$ de $4$ .

$\frac{\frac{2 e^{x^{2}} (84 x^{4} + 21 x^{3} + 72 x^{5} + 18 x^{4} + 140 x^{3} + 123 x^{2} - 18 x^{3} - 21 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.31

Some $84 x^{4}$ e $18 x^{4}$ .

$\frac{\frac{2 e^{x^{2}} (102 x^{4} + 21 x^{3} + 72 x^{5} + 140 x^{3} + 123 x^{2} - 18 x^{3} - 21 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.32

Some $21 x^{3}$ e $140 x^{3}$ .

$\frac{\frac{2 e^{x^{2}} (102 x^{4} + 72 x^{5} + 161 x^{3} + 123 x^{2} - 18 x^{3} - 21 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.33

Subtraia $18 x^{3}$ de $161 x^{3}$ .

$\frac{\frac{2 e^{x^{2}} (102 x^{4} + 72 x^{5} + 143 x^{3} + 123 x^{2} - 21 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.34

Subtraia $21 x^{2}$ de $123 x^{2}$ .

$\frac{\frac{2 e^{x^{2}} (102 x^{4} + 72 x^{5} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.6.23.35

Reordene os termos.

$\frac{\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.7

Combine os termos.

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Etapa 4.31.7.1

Multiplique $e^{x^{2}}$ por $1$ .

$\frac{\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.7.2

Reescreva $\frac{\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$ como um produto.

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}} \cdot \frac{1}{(e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$

Etapa 4.31.7.3

Multiplique $\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}$ por $\frac{1}{(e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$ .

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}})}$

Etapa 4.31.7.4

Multiplique ${(4 x + 1)}^{\frac{1}{2}}$ por ${(4 x + 1)}^{\frac{1}{2}}$ somando os expoentes.

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Etapa 4.31.7.4.1

Mova ${(4 x + 1)}^{\frac{1}{2}}$ .

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2})}$

Etapa 4.31.7.4.2

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

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2} + \frac{1}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2})}$

Etapa 4.31.7.4.3

Combine os numeradores em relação ao denominador comum.

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1 + 1}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2})}$

Etapa 4.31.7.4.4

Some $1$ e $1$ .

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{2}{2}} ((e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2})}$

Etapa 4.31.7.4.5

Divida $2$ por $2$ .

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{1} ((e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2})}$

Etapa 4.31.7.5

Simplifique ${(4 x + 1)}^{1} ((e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2})$ .

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{(4 x + 1) (e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2}}$

Etapa 4.31.8

Reordene os termos.

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(3 x + 1)}^{2} (4 x + 1) (e^{x^{2}} (2 x) + e^{x^{2}})}$

Etapa 4.31.9

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

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Etapa 4.31.9.1

Multiplique por $1$ .

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(3 x + 1)}^{2} (4 x + 1) (e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1)}$

Etapa 4.31.9.2

Fatore $e^{x^{2}}$ de $e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1$ .

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(3 x + 1)}^{2} (4 x + 1) (e^{x^{2}} (2 x + 1))}$

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(3 x + 1)}^{2} (4 x + 1) e^{x^{2}} (2 x + 1)}$

Etapa 4.31.10

Cancele o fator comum de $e^{x^{2}}$ .

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Etapa 4.31.10.1

Cancele o fator comum.

$\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(3 x + 1)}^{2} (4 x + 1) e^{x^{2}} (2 x + 1)}$

Etapa 4.31.10.2

Reescreva a expressão.

$\frac{2 (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(3 x + 1)}^{2} (4 x + 1) (2 x + 1)}$

Etapa 5

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

$y' = \frac{2 (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(3 x + 1)}^{2} (4 x + 1) (2 x + 1)}$

Etapa 6

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

$\frac{d y}{d x} = \frac{2 (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(3 x + 1)}^{2} (4 x + 1) (2 x + 1)}$