Analysis Beispiele

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

Schritt 1

Benutze $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ , um $\sqrt{4 x + 1}$ als ${(4 x + 1)}^{\frac{1}{2}}$ neu zu schreiben.

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

Schritt 2

Differenziere beide Seiten der Gleichung.

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

Schritt 3

Die Ableitung von $y$ nach $x$ ist $y'$ .

$y'$

Schritt 4

Differenziere die rechte Seite der Gleichung.

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Schritt 4.1

Differenziere unter Anwendung der Kettenregel, die besagt, dass $\frac{d}{d x} [f (g (x))]$ ist $f' (g (x)) g' (x)$ , mit $f (x) = \ln (x)$ und $g (x) = \frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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Schritt 4.1.1

Um die Kettenregel anzuwenden, ersetze $u_{1}$ durch $\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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

Schritt 4.1.2

Die Ableitung von $\ln (u_{1})$ nach $u_{1}$ ist $\frac{1}{u_{1}}$ .

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

Schritt 4.1.3

Ersetze alle $u_{1}$ durch $\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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

Schritt 4.2

Multipliziere mit dem Kehrwert des Bruchs, um durch $\frac{e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}}{{(4 x + 1)}^{\frac{1}{2}}}$ zu dividieren.

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

Schritt 4.3

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

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

Schritt 4.4

Differenziere unter Anwendung der Quotientenregel, die besagt, dass $\frac{d}{d x} [\frac{f (x)}{g (x)}]$ gleich $\frac{g (x) \frac{d}{d x} [f (x)] - f (x) \frac{d}{d x} [g (x)]}{{g (x)}^{2}}$ ist mit $f (x) = e^{x^{2}} (2 x + 1) {(3 x + 1)}^{2}$ und $g (x) = {(4 x + 1)}^{\frac{1}{2}}$ .

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

Schritt 4.5

Multipliziere die Exponenten in ${({(4 x + 1)}^{\frac{1}{2}})}^{2}$ .

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Schritt 4.5.1

Wende die Potenzregel an und multipliziere die Exponenten, ${(a^{m})}^{n} = a^{m n}$ .

Schritt 4.5.2

Kürze den gemeinsamen Faktor von $2$ .

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Schritt 4.5.2.1

Kürze den gemeinsamen Faktor.

Schritt 4.5.2.2

Forme den Ausdruck um.

Schritt 4.6

Vereinfache.

Schritt 4.7

Differenziere unter Anwendung der Produktregel, die besagt, dass $\frac{d}{d x} [f (x) g (x)]$ gleich $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ ist mit $f (x) = e^{x^{2}} (2 x + 1)$ und $g (x) = {(3 x + 1)}^{2}$ .

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

Schritt 4.8

Differenziere unter Anwendung der Kettenregel, die besagt, dass $\frac{d}{d x} [f (g (x))]$ ist $f' (g (x)) g' (x)$ , mit $f (x) = x^{2}$ und $g (x) = 3 x + 1$ .

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Schritt 4.8.1

Um die Kettenregel anzuwenden, ersetze $u_{2}$ durch $3 x + 1$ .

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

Schritt 4.8.2

Differenziere unter Anwendung der Potenzregel, die besagt, dass $\frac{d}{d u_{2}} [{u_{2}}^{n}]$ gleich $n {u_{2}}^{n - 1}$ ist mit $n = 2$ .

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

Schritt 4.8.3

Ersetze alle $u_{2}$ durch $3 x + 1$ .

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

Schritt 4.9

Differenziere.

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Schritt 4.9.1

Gemäß der Summenregel ist die Ableitung von $3 x + 1$ nach $x$ $\frac{d}{d x} [3 x] + \frac{d}{d x} [1]$ .

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

Schritt 4.9.2

Da $3$ konstant bezüglich $x$ ist, ist die Ableitung von $3 x$ nach $x$ gleich $3 \frac{d}{d x} [x]$ .

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

Schritt 4.9.3

Differenziere unter Anwendung der Potenzregel, die besagt, dass $\frac{d}{d x} [x^{n}]$ gleich $n x^{n - 1}$ ist mit $n = 1$ .

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

Schritt 4.9.4

Mutltipliziere $3$ mit $1$ .

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

Schritt 4.9.5

Da $1$ konstant bezüglich $x$ ist, ist die Ableitung von $1$ bezüglich $x$ gleich $0$ .

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

Schritt 4.9.6

Vereinfache den Ausdruck.

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Schritt 4.9.6.1

Addiere $3$ und $0$ .

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

Schritt 4.9.6.2

Mutltipliziere $3$ mit $2$ .

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

Schritt 4.10

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

Schritt 4.11

Differenziere.

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Schritt 4.11.1

Gemäß der Summenregel ist die Ableitung von $2 x + 1$ nach $x$ $\frac{d}{d x} [2 x] + \frac{d}{d x} [1]$ .

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

Schritt 4.11.2

Da $2$ konstant bezüglich $x$ ist, ist die Ableitung von $2 x$ nach $x$ gleich $2 \frac{d}{d x} [x]$ .

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

Schritt 4.11.3

Differenziere unter Anwendung der Potenzregel, die besagt, dass $\frac{d}{d x} [x^{n}]$ gleich $n x^{n - 1}$ ist mit $n = 1$ .

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

Schritt 4.11.4

Mutltipliziere $2$ mit $1$ .

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

Schritt 4.11.5

Da $1$ konstant bezüglich $x$ ist, ist die Ableitung von $1$ bezüglich $x$ gleich $0$ .

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

Schritt 4.11.6

Vereinfache den Ausdruck.

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Schritt 4.11.6.1

Addiere $2$ und $0$ .

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

Schritt 4.11.6.2

Bringe $2$ auf die linke Seite von $e^{x^{2}}$ .

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

Schritt 4.12

Differenziere unter Anwendung der Kettenregel, die besagt, dass $\frac{d}{d x} [f (g (x))]$ ist $f' (g (x)) g' (x)$ , mit $f (x) = e^{x}$ und $g (x) = x^{2}$ .

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Schritt 4.12.1

Um die Kettenregel anzuwenden, ersetze $u_{3}$ durch $x^{2}$ .

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

Schritt 4.12.2

Differenziere unter Anwendung der Exponentialregel, die besagt, dass $\frac{d}{d u_{3}} [a^{u_{3}}]$ gleich $a^{u_{3}} \ln (a)$ ist, wobei $a$ = $e$ .

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

Schritt 4.12.3

Ersetze alle $u_{3}$ durch $x^{2}$ .

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

Schritt 4.13

Differenziere unter Anwendung der Potenzregel, die besagt, dass $\frac{d}{d x} [x^{n}]$ gleich $n x^{n - 1}$ ist mit $n = 2$ .

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

Schritt 4.14

Differenziere unter Anwendung der Kettenregel, die besagt, dass $\frac{d}{d x} [f (g (x))]$ ist $f' (g (x)) g' (x)$ , mit $f (x) = x^{\frac{1}{2}}$ und $g (x) = 4 x + 1$ .

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Schritt 4.14.1

Um die Kettenregel anzuwenden, ersetze $u_{4}$ durch $4 x + 1$ .

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

Schritt 4.14.2

Differenziere unter Anwendung der Potenzregel, die besagt, dass $\frac{d}{d u_{4}} [{u_{4}}^{n}]$ gleich $n {u_{4}}^{n - 1}$ ist mit $n = \frac{1}{2}$ .

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

Schritt 4.14.3

Ersetze alle $u_{4}$ durch $4 x + 1$ .

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

Schritt 4.15

Um $- 1$ als Bruch mit einem gemeinsamen Nenner zu schreiben, multipliziere mit $\frac{2}{2}$ .

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

Schritt 4.16

Kombiniere $- 1$ und $\frac{2}{2}$ .

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

Schritt 4.17

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.18

Vereinfache den Zähler.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.18.1

Mutltipliziere $- 1$ mit $2$ .

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

Schritt 4.18.2

Subtrahiere $2$ von $1$ .

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

Schritt 4.19

Kombiniere Brüche.

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Schritt 4.19.1

Ziehe das Minuszeichen vor den Bruch.

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

Schritt 4.19.2

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

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

Schritt 4.19.3

Bringe ${(4 x + 1)}^{- \frac{1}{2}}$ in den Nenner mit Hilfe der Regel des negativen Exponenten $b^{- n} = \frac{1}{b^{n}}$ .

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

Schritt 4.19.4

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

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

Schritt 4.19.5

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

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

Schritt 4.20

Gemäß der Summenregel ist die Ableitung von $4 x + 1$ nach $x$ $\frac{d}{d x} [4 x] + \frac{d}{d x} [1]$ .

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

Schritt 4.21

Da $4$ konstant bezüglich $x$ ist, ist die Ableitung von $4 x$ nach $x$ gleich $4 \frac{d}{d x} [x]$ .

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

Schritt 4.22

Differenziere unter Anwendung der Potenzregel, die besagt, dass $\frac{d}{d x} [x^{n}]$ gleich $n x^{n - 1}$ ist mit $n = 1$ .

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

Schritt 4.23

Mutltipliziere $4$ mit $1$ .

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

Schritt 4.24

Da $1$ konstant bezüglich $x$ ist, ist die Ableitung von $1$ bezüglich $x$ gleich $0$ .

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

Schritt 4.25

Vereinfache Terme.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.25.1

Addiere $4$ und $0$ .

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

Schritt 4.25.2

Mutltipliziere $4$ mit $- 1$ .

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

Schritt 4.25.3

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

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

Schritt 4.25.4

Faktorisiere $2$ aus $- 4 {(3 x + 1)}^{2} e^{x^{2}}$ heraus.

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

Schritt 4.26

Kürze die gemeinsamen Faktoren.

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Schritt 4.26.1

Faktorisiere $2$ aus $2 {(4 x + 1)}^{\frac{1}{2}}$ heraus.

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

Schritt 4.26.2

Kürze den gemeinsamen Faktor.

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

Schritt 4.26.3

Forme den Ausdruck um.

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

Schritt 4.27

Ziehe das Minuszeichen vor den Bruch.

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

Schritt 4.28

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

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

Schritt 4.29

Bringe ${(4 x + 1)}^{\frac{1}{2}}$ in den Nenner mit Hilfe der Regel des negativen Exponenten $b^{n} = \frac{1}{b^{- n}}$ .

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

Schritt 4.30

Multipliziere $4 x + 1$ mit ${(4 x + 1)}^{- \frac{1}{2}}$ durch Addieren der Exponenten.

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Schritt 4.30.1

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

Schritt 4.30.2

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

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Schritt 4.30.2.1

Potenziere $4 x + 1$ mit $1$ .

Schritt 4.30.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

Schritt 4.30.3

Schreibe $1$ als Bruch mit einem gemeinsamen Nenner.

Schritt 4.30.4

Vereinige die Zähler über dem gemeinsamen Nenner.

Schritt 4.30.5

Addiere $- 1$ und $2$ .

Schritt 4.31

Vereinfache.

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Schritt 4.31.1

Wende das Distributivgesetz an.

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

Schritt 4.31.2

Wende das Distributivgesetz an.

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

Schritt 4.31.3

Wende das Distributivgesetz an.

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

Schritt 4.31.4

Wende das Distributivgesetz an.

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

Schritt 4.31.5

Wende das Distributivgesetz an.

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

Schritt 4.31.6

Vereinfache den Zähler.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1.1

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1.1.1

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.1.2

Mutltipliziere $e^{x^{2}}$ mit $1$ .

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

Schritt 4.31.6.1.2

Vereinfache jeden Term.

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Schritt 4.31.6.1.2.1

Mutltipliziere $3$ mit $6$ .

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

Schritt 4.31.6.1.2.2

Mutltipliziere $6$ mit $1$ .

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

Schritt 4.31.6.1.3

Multipliziere $(2 e^{x^{2}} x + e^{x^{2}}) (18 x + 6)$ aus unter Verwendung der FOIL-Methode.

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Schritt 4.31.6.1.3.1

Wende das Distributivgesetz an.

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

Schritt 4.31.6.1.3.2

Wende das Distributivgesetz an.

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

Schritt 4.31.6.1.3.3

Wende das Distributivgesetz an.

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

Schritt 4.31.6.1.4

Vereinfache und fasse gleichartige Terme zusammen.

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Schritt 4.31.6.1.4.1

Vereinfache jeden Term.

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Schritt 4.31.6.1.4.1.1

Multipliziere $x$ mit $x$ durch Addieren der Exponenten.

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Schritt 4.31.6.1.4.1.1.1

Bewege $x$ .

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

Schritt 4.31.6.1.4.1.1.2

Mutltipliziere $x$ mit $x$ .

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

Schritt 4.31.6.1.4.1.2

Mutltipliziere $18$ mit $2$ .

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

Schritt 4.31.6.1.4.1.3

Mutltipliziere $6$ mit $2$ .

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

Schritt 4.31.6.1.4.1.4

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.4.1.5

Bringe $6$ auf die linke Seite von $e^{x^{2}}$ .

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

Schritt 4.31.6.1.4.2

Addiere $12 e^{x^{2}} x$ und $18 e^{x^{2}} x$ .

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

Schritt 4.31.6.1.5

Schreibe ${(3 x + 1)}^{2}$ als $(3 x + 1) (3 x + 1)$ um.

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

Schritt 4.31.6.1.6

Multipliziere $(3 x + 1) (3 x + 1)$ aus unter Verwendung der FOIL-Methode.

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Schritt 4.31.6.1.6.1

Wende das Distributivgesetz an.

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

Schritt 4.31.6.1.6.2

Wende das Distributivgesetz an.

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

Schritt 4.31.6.1.6.3

Wende das Distributivgesetz an.

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

Schritt 4.31.6.1.7

Vereinfache und fasse gleichartige Terme zusammen.

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Schritt 4.31.6.1.7.1

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1.7.1.1

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.7.1.2

Multipliziere $x$ mit $x$ durch Addieren der Exponenten.

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Schritt 4.31.6.1.7.1.2.1

Bewege $x$ .

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

Schritt 4.31.6.1.7.1.2.2

Mutltipliziere $x$ mit $x$ .

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

Schritt 4.31.6.1.7.1.3

Mutltipliziere $3$ mit $3$ .

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

Schritt 4.31.6.1.7.1.4

Mutltipliziere $3$ mit $1$ .

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

Schritt 4.31.6.1.7.1.5

Mutltipliziere $3 x$ mit $1$ .

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

Schritt 4.31.6.1.7.1.6

Mutltipliziere $1$ mit $1$ .

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

Schritt 4.31.6.1.7.2

Addiere $3 x$ und $3 x$ .

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

Schritt 4.31.6.1.8

Vereinfache jeden Term.

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Schritt 4.31.6.1.8.1

Multipliziere $x$ mit $x$ durch Addieren der Exponenten.

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Schritt 4.31.6.1.8.1.1

Bewege $x$ .

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

Schritt 4.31.6.1.8.1.2

Mutltipliziere $x$ mit $x$ .

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

Schritt 4.31.6.1.8.2

Mutltipliziere $2$ mit $2$ .

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

Schritt 4.31.6.1.8.3

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.8.4

Mutltipliziere $2$ mit $1$ .

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

Schritt 4.31.6.1.9

Multipliziere $(9 x^{2} + 6 x + 1) (2 e^{x^{2}} + 4 x^{2} e^{x^{2}} + 2 e^{x^{2}} x)$ aus durch Multiplizieren jedes Terms des ersten Ausdrucks mit jedem Term des zweiten Ausdrucks.

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

Schritt 4.31.6.1.10

Vereinfache jeden Term.

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Schritt 4.31.6.1.10.1

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.10.2

Mutltipliziere $9$ mit $2$ .

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

Schritt 4.31.6.1.10.3

Multipliziere $x^{2}$ mit $x^{2}$ durch Addieren der Exponenten.

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Schritt 4.31.6.1.10.3.1

Bewege $x^{2}$ .

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

Schritt 4.31.6.1.10.3.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.1.10.3.3

Addiere $2$ und $2$ .

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

Schritt 4.31.6.1.10.4

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.10.5

Mutltipliziere $9$ mit $4$ .

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

Schritt 4.31.6.1.10.6

Multipliziere $x^{2}$ mit $x$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1.10.6.1

Bewege $x$ .

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

Schritt 4.31.6.1.10.6.2

Mutltipliziere $x$ mit $x^{2}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1.10.6.2.1

Potenziere $x$ mit $1$ .

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

Schritt 4.31.6.1.10.6.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.1.10.6.3

Addiere $1$ und $2$ .

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

Schritt 4.31.6.1.10.7

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.10.8

Mutltipliziere $9$ mit $2$ .

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

Schritt 4.31.6.1.10.9

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.10.10

Mutltipliziere $6$ mit $2$ .

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

Schritt 4.31.6.1.10.11

Multipliziere $x$ mit $x^{2}$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1.10.11.1

Bewege $x^{2}$ .

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

Schritt 4.31.6.1.10.11.2

Mutltipliziere $x^{2}$ mit $x$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1.10.11.2.1

Potenziere $x$ mit $1$ .

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

Schritt 4.31.6.1.10.11.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.1.10.11.3

Addiere $2$ und $1$ .

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

Schritt 4.31.6.1.10.12

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.10.13

Mutltipliziere $6$ mit $4$ .

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

Schritt 4.31.6.1.10.14

Multipliziere $x$ mit $x$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1.10.14.1

Bewege $x$ .

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

Schritt 4.31.6.1.10.14.2

Mutltipliziere $x$ mit $x$ .

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

Schritt 4.31.6.1.10.15

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.1.10.16

Mutltipliziere $6$ mit $2$ .

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

Schritt 4.31.6.1.10.17

Mutltipliziere $2 e^{x^{2}}$ mit $1$ .

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

Schritt 4.31.6.1.10.18

Mutltipliziere $4 x^{2} e^{x^{2}}$ mit $1$ .

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

Schritt 4.31.6.1.10.19

Mutltipliziere $2 e^{x^{2}} x$ mit $1$ .

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

Schritt 4.31.6.1.11

Addiere $18 x^{2} e^{x^{2}}$ und $12 x^{2} e^{x^{2}}$ .

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

Schritt 4.31.6.1.12

Addiere $30 x^{2} e^{x^{2}}$ und $4 x^{2} e^{x^{2}}$ .

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

Schritt 4.31.6.1.13

Addiere $18 x^{3} e^{x^{2}}$ und $24 x^{3} e^{x^{2}}$ .

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

Schritt 4.31.6.1.14

Addiere $12 x e^{x^{2}}$ und $2 e^{x^{2}} x$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.1.14.1

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

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

Schritt 4.31.6.1.14.2

Addiere $12 x e^{x^{2}}$ und $2 x e^{x^{2}}$ .

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

Schritt 4.31.6.2

Addiere $36 e^{x^{2}} x^{2}$ und $34 x^{2} e^{x^{2}}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.2.1

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

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

Schritt 4.31.6.2.2

Addiere $36 x^{2} e^{x^{2}}$ und $34 x^{2} e^{x^{2}}$ .

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

Schritt 4.31.6.3

Addiere $30 e^{x^{2}} x$ und $14 x e^{x^{2}}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.3.1

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

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

Schritt 4.31.6.3.2

Addiere $30 x e^{x^{2}}$ und $14 x e^{x^{2}}$ .

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

Schritt 4.31.6.4

Addiere $6 e^{x^{2}}$ und $2 e^{x^{2}}$ .

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

Schritt 4.31.6.5

Wende das Distributivgesetz an.

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

Schritt 4.31.6.6

Vereinfache.

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Schritt 4.31.6.6.1

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.6.2

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.6.3

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.6.4

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.6.5

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.7

Wende das Distributivgesetz an.

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

Schritt 4.31.6.8

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

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Schritt 4.31.6.8.1

Mutltipliziere $2$ mit $- 1$ .

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

Schritt 4.31.6.8.2

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

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

Schritt 4.31.6.8.3

Mutltipliziere $2$ mit $- 2$ .

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

Schritt 4.31.6.8.4

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

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

Schritt 4.31.6.9

Mutltipliziere $- 1$ mit $1$ .

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

Schritt 4.31.6.10

Ziehe das Minuszeichen vor den Bruch.

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

Schritt 4.31.6.11

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.12

Faktorisiere $2 {(3 x + 1)}^{2} e^{x^{2}}$ aus $- 4 {(3 x + 1)}^{2} e^{x^{2}} x - 2 {(3 x + 1)}^{2} e^{x^{2}}$ heraus.

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Schritt 4.31.6.12.1

Faktorisiere $2 {(3 x + 1)}^{2} e^{x^{2}}$ aus $- 4 {(3 x + 1)}^{2} e^{x^{2}} x$ heraus.

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

Schritt 4.31.6.12.2

Faktorisiere $2 {(3 x + 1)}^{2} e^{x^{2}}$ aus $- 2 {(3 x + 1)}^{2} e^{x^{2}}$ heraus.

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

Schritt 4.31.6.12.3

Faktorisiere $2 {(3 x + 1)}^{2} e^{x^{2}}$ aus $2 {(3 x + 1)}^{2} e^{x^{2}} (- 2 x) + 2 {(3 x + 1)}^{2} e^{x^{2}} (- 1)$ heraus.

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

Schritt 4.31.6.13

Um $70 {(4 x + 1)}^{\frac{1}{2}} x^{2} e^{x^{2}}$ als Bruch mit einem gemeinsamen Nenner zu schreiben, multipliziere mit $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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

Schritt 4.31.6.14

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.15

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

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

Schritt 4.31.6.16

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

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Schritt 4.31.6.16.1

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

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

Schritt 4.31.6.16.2

Um $36 x^{4} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}}$ als Bruch mit einem gemeinsamen Nenner zu schreiben, multipliziere mit $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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

Schritt 4.31.6.16.3

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.17

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

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Schritt 4.31.6.17.1

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

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

Schritt 4.31.6.17.2

Um $42 x^{3} e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}}$ als Bruch mit einem gemeinsamen Nenner zu schreiben, multipliziere mit $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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

Schritt 4.31.6.17.3

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.18

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

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Schritt 4.31.6.18.1

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

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

Schritt 4.31.6.18.2

Um $8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}}$ als Bruch mit einem gemeinsamen Nenner zu schreiben, multipliziere mit $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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

Schritt 4.31.6.18.3

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.19

Um $44 x e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}}$ als Bruch mit einem gemeinsamen Nenner zu schreiben, multipliziere mit $\frac{{(4 x + 1)}^{\frac{1}{2}}}{{(4 x + 1)}^{\frac{1}{2}}}$ .

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

Schritt 4.31.6.20

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.21

Stelle die Terme um.

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

Schritt 4.31.6.22

Schreibe $\frac{44 e^{x^{2}} x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 42 e^{x^{2}} x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 36 e^{x^{2}} x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)}{{(4 x + 1)}^{\frac{1}{2}}}$ in eine faktorisierte Form um.

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Schritt 4.31.6.22.1

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

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Schritt 4.31.6.22.1.1

Faktorisiere $2 e^{x^{2}}$ aus $44 e^{x^{2}} x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ heraus.

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

Schritt 4.31.6.22.1.2

Faktorisiere $2 e^{x^{2}}$ aus $8 e^{x^{2}} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ heraus.

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

Schritt 4.31.6.22.1.3

Faktorisiere $2 e^{x^{2}}$ aus $42 e^{x^{2}} x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ heraus.

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

Schritt 4.31.6.22.1.4

Faktorisiere $2 e^{x^{2}}$ aus $36 e^{x^{2}} x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ heraus.

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

Schritt 4.31.6.22.1.5

Faktorisiere $2 e^{x^{2}}$ aus $70 e^{x^{2}} x^{2} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}$ heraus.

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

Schritt 4.31.6.22.1.6

Faktorisiere $2 e^{x^{2}}$ aus $2 e^{x^{2}} {(3 x + 1)}^{2} (- 2 x - 1)$ heraus.

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

Schritt 4.31.6.22.1.7

Faktorisiere $2 e^{x^{2}}$ aus $2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}})$ heraus.

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

Schritt 4.31.6.22.1.8

Faktorisiere $2 e^{x^{2}}$ aus $2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}})$ heraus.

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

Schritt 4.31.6.22.1.9

Faktorisiere $2 e^{x^{2}}$ aus $2 e^{x^{2}} (22 x {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 4 {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}} + 21 x^{3} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}}) + 2 e^{x^{2}} (18 x^{4} {(4 x + 1)}^{\frac{1}{2}} {(4 x + 1)}^{\frac{1}{2}})$ heraus.

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

Schritt 4.31.6.22.1.10

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

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

Schritt 4.31.6.22.1.11

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

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

Schritt 4.31.6.22.2

Kombiniere Exponenten.

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Schritt 4.31.6.22.2.1

Multipliziere ${(4 x + 1)}^{\frac{1}{2}}$ mit ${(4 x + 1)}^{\frac{1}{2}}$ durch Addieren der Exponenten.

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Schritt 4.31.6.22.2.1.1

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

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

Schritt 4.31.6.22.2.1.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.22.2.1.3

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.22.2.1.4

Addiere $1$ und $1$ .

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

Schritt 4.31.6.22.2.1.5

Dividiere $2$ durch $2$ .

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

Schritt 4.31.6.22.2.2

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

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

Schritt 4.31.6.22.2.3

Multipliziere ${(4 x + 1)}^{\frac{1}{2}}$ mit ${(4 x + 1)}^{\frac{1}{2}}$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.22.2.3.1

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

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

Schritt 4.31.6.22.2.3.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.22.2.3.3

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.22.2.3.4

Addiere $1$ und $1$ .

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

Schritt 4.31.6.22.2.3.5

Dividiere $2$ durch $2$ .

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

Schritt 4.31.6.22.2.4

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

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

Schritt 4.31.6.22.2.5

Multipliziere ${(4 x + 1)}^{\frac{1}{2}}$ mit ${(4 x + 1)}^{\frac{1}{2}}$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.22.2.5.1

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

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

Schritt 4.31.6.22.2.5.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.22.2.5.3

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.22.2.5.4

Addiere $1$ und $1$ .

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

Schritt 4.31.6.22.2.5.5

Dividiere $2$ durch $2$ .

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

Schritt 4.31.6.22.2.6

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

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

Schritt 4.31.6.22.2.7

Multipliziere ${(4 x + 1)}^{\frac{1}{2}}$ mit ${(4 x + 1)}^{\frac{1}{2}}$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.22.2.7.1

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

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

Schritt 4.31.6.22.2.7.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.22.2.7.3

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.22.2.7.4

Addiere $1$ und $1$ .

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

Schritt 4.31.6.22.2.7.5

Dividiere $2$ durch $2$ .

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

Schritt 4.31.6.22.2.8

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

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

Schritt 4.31.6.22.2.9

Multipliziere ${(4 x + 1)}^{\frac{1}{2}}$ mit ${(4 x + 1)}^{\frac{1}{2}}$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.22.2.9.1

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

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

Schritt 4.31.6.22.2.9.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.22.2.9.3

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.6.22.2.9.4

Addiere $1$ und $1$ .

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

Schritt 4.31.6.22.2.9.5

Dividiere $2$ durch $2$ .

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

Schritt 4.31.6.22.2.10

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

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

Schritt 4.31.6.23

Vereinfache den Zähler.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.1

Wende das Distributivgesetz an.

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

Schritt 4.31.6.23.2

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.23.3

Mutltipliziere $22$ mit $1$ .

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

Schritt 4.31.6.23.4

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.4.1

Multipliziere $x$ mit $x$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.4.1.1

Bewege $x$ .

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

Schritt 4.31.6.23.4.1.2

Mutltipliziere $x$ mit $x$ .

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

Schritt 4.31.6.23.4.2

Mutltipliziere $22$ mit $4$ .

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

Schritt 4.31.6.23.5

Wende das Distributivgesetz an.

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

Schritt 4.31.6.23.6

Mutltipliziere $4$ mit $4$ .

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

Schritt 4.31.6.23.7

Mutltipliziere $4$ mit $1$ .

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

Schritt 4.31.6.23.8

Wende das Distributivgesetz an.

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

Schritt 4.31.6.23.9

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.23.10

Mutltipliziere $21$ mit $1$ .

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

Schritt 4.31.6.23.11

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.11.1

Multipliziere $x^{3}$ mit $x$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.11.1.1

Bewege $x$ .

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

Schritt 4.31.6.23.11.1.2

Mutltipliziere $x$ mit $x^{3}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.11.1.2.1

Potenziere $x$ mit $1$ .

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

Schritt 4.31.6.23.11.1.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.23.11.1.3

Addiere $1$ und $3$ .

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

Schritt 4.31.6.23.11.2

Mutltipliziere $21$ mit $4$ .

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

Schritt 4.31.6.23.12

Wende das Distributivgesetz an.

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

Schritt 4.31.6.23.13

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.23.14

Mutltipliziere $18$ mit $1$ .

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

Schritt 4.31.6.23.15

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.15.1

Multipliziere $x^{4}$ mit $x$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.15.1.1

Bewege $x$ .

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

Schritt 4.31.6.23.15.1.2

Mutltipliziere $x$ mit $x^{4}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.15.1.2.1

Potenziere $x$ mit $1$ .

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

Schritt 4.31.6.23.15.1.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.23.15.1.3

Addiere $1$ und $4$ .

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

Schritt 4.31.6.23.15.2

Mutltipliziere $18$ mit $4$ .

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

Schritt 4.31.6.23.16

Wende das Distributivgesetz an.

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

Schritt 4.31.6.23.17

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.23.18

Mutltipliziere $35$ mit $1$ .

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

Schritt 4.31.6.23.19

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.19.1

Multipliziere $x^{2}$ mit $x$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.19.1.1

Bewege $x$ .

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

Schritt 4.31.6.23.19.1.2

Mutltipliziere $x$ mit $x^{2}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.19.1.2.1

Potenziere $x$ mit $1$ .

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

Schritt 4.31.6.23.19.1.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.23.19.1.3

Addiere $1$ und $2$ .

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

Schritt 4.31.6.23.19.2

Mutltipliziere $35$ mit $4$ .

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

Schritt 4.31.6.23.20

Schreibe ${(3 x + 1)}^{2}$ als $(3 x + 1) (3 x + 1)$ um.

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

Schritt 4.31.6.23.21

Multipliziere $(3 x + 1) (3 x + 1)$ aus unter Verwendung der FOIL-Methode.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.21.1

Wende das Distributivgesetz an.

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

Schritt 4.31.6.23.21.2

Wende das Distributivgesetz an.

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

Schritt 4.31.6.23.21.3

Wende das Distributivgesetz an.

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

Schritt 4.31.6.23.22

Vereinfache und fasse gleichartige Terme zusammen.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.22.1

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.22.1.1

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.23.22.1.2

Multipliziere $x$ mit $x$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.22.1.2.1

Bewege $x$ .

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

Schritt 4.31.6.23.22.1.2.2

Mutltipliziere $x$ mit $x$ .

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

Schritt 4.31.6.23.22.1.3

Mutltipliziere $3$ mit $3$ .

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

Schritt 4.31.6.23.22.1.4

Mutltipliziere $3$ mit $1$ .

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

Schritt 4.31.6.23.22.1.5

Mutltipliziere $3 x$ mit $1$ .

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

Schritt 4.31.6.23.22.1.6

Mutltipliziere $1$ mit $1$ .

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

Schritt 4.31.6.23.22.2

Addiere $3 x$ und $3 x$ .

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

Schritt 4.31.6.23.23

Multipliziere $(9 x^{2} + 6 x + 1) (- 2 x - 1)$ aus durch Multiplizieren jedes Terms des ersten Ausdrucks mit jedem Term des zweiten Ausdrucks.

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

Schritt 4.31.6.23.24

Vereinfache jeden Term.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.24.1

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.23.24.2

Multipliziere $x^{2}$ mit $x$ durch Addieren der Exponenten.

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.24.2.1

Bewege $x$ .

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

Schritt 4.31.6.23.24.2.2

Mutltipliziere $x$ mit $x^{2}$ .

Tippen, um mehr Schritte zu sehen ...

Schritt 4.31.6.23.24.2.2.1

Potenziere $x$ mit $1$ .

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

Schritt 4.31.6.23.24.2.2.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.6.23.24.2.3

Addiere $1$ und $2$ .

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

Schritt 4.31.6.23.24.3

Mutltipliziere $9$ mit $- 2$ .

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

Schritt 4.31.6.23.24.4

Mutltipliziere $- 1$ mit $9$ .

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

Schritt 4.31.6.23.24.5

Schreibe neu unter Anwendung des Kommutativgesetzes der Multiplikation.

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

Schritt 4.31.6.23.24.6

Multipliziere $x$ mit $x$ durch Addieren der Exponenten.

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Schritt 4.31.6.23.24.6.1

Bewege $x$ .

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

Schritt 4.31.6.23.24.6.2

Mutltipliziere $x$ mit $x$ .

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

Schritt 4.31.6.23.24.7

Mutltipliziere $6$ mit $- 2$ .

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

Schritt 4.31.6.23.24.8

Mutltipliziere $- 1$ mit $6$ .

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

Schritt 4.31.6.23.24.9

Mutltipliziere $- 2 x$ mit $1$ .

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

Schritt 4.31.6.23.24.10

Mutltipliziere $- 1$ mit $1$ .

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

Schritt 4.31.6.23.25

Subtrahiere $12 x^{2}$ von $- 9 x^{2}$ .

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

Schritt 4.31.6.23.26

Subtrahiere $2 x$ von $- 6 x$ .

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

Schritt 4.31.6.23.27

Addiere $88 x^{2}$ und $35 x^{2}$ .

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

Schritt 4.31.6.23.28

Addiere $22 x$ und $16 x$ .

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

Schritt 4.31.6.23.29

Subtrahiere $8 x$ von $38 x$ .

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

Schritt 4.31.6.23.30

Subtrahiere $1$ von $4$ .

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

Schritt 4.31.6.23.31

Addiere $84 x^{4}$ und $18 x^{4}$ .

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

Schritt 4.31.6.23.32

Addiere $21 x^{3}$ und $140 x^{3}$ .

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

Schritt 4.31.6.23.33

Subtrahiere $18 x^{3}$ von $161 x^{3}$ .

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

Schritt 4.31.6.23.34

Subtrahiere $21 x^{2}$ von $123 x^{2}$ .

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

Schritt 4.31.6.23.35

Stelle die Terme um.

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

Schritt 4.31.7

Vereine die Terme

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Schritt 4.31.7.1

Mutltipliziere $e^{x^{2}}$ mit $1$ .

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

Schritt 4.31.7.2

Schreibe $\frac{\frac{2 e^{x^{2}} (72 x^{5} + 102 x^{4} + 143 x^{3} + 102 x^{2} + 30 x + 3)}{{(4 x + 1)}^{\frac{1}{2}}}}{(e^{x^{2}} (2 x) + e^{x^{2}}) {(3 x + 1)}^{2} {(4 x + 1)}^{\frac{1}{2}}}$ als ein Produkt um.

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

Schritt 4.31.7.3

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

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

Schritt 4.31.7.4

Multipliziere ${(4 x + 1)}^{\frac{1}{2}}$ mit ${(4 x + 1)}^{\frac{1}{2}}$ durch Addieren der Exponenten.

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Schritt 4.31.7.4.1

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

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

Schritt 4.31.7.4.2

Wende die Exponentenregel $a^{m} a^{n} = a^{m + n}$ an, um die Exponenten zu kombinieren.

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

Schritt 4.31.7.4.3

Vereinige die Zähler über dem gemeinsamen Nenner.

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

Schritt 4.31.7.4.4

Addiere $1$ und $1$ .

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

Schritt 4.31.7.4.5

Dividiere $2$ durch $2$ .

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

Schritt 4.31.7.5

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

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

Schritt 4.31.8

Stelle die Terme um.

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

Schritt 4.31.9

Faktorisiere $e^{x^{2}}$ aus $e^{x^{2}} (2 x) + e^{x^{2}}$ heraus.

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Schritt 4.31.9.1

Multipliziere mit $1$ .

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

Schritt 4.31.9.2

Faktorisiere $e^{x^{2}}$ aus $e^{x^{2}} (2 x) + e^{x^{2}} \cdot 1$ heraus.

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

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

Schritt 4.31.10

Kürze den gemeinsamen Faktor von $e^{x^{2}}$ .

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Schritt 4.31.10.1

Kürze den gemeinsamen Faktor.

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

Schritt 4.31.10.2

Forme den Ausdruck um.

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

Schritt 5

Forme die Gleichung um durch Gleichsetzen der linken Seite mit der rechten Seite.

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

Schritt 6

Ersetze $y'$ durch $\frac{d y}{d x}$ .

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