derivative of 2\sqrt[3]{x^7}

Lösung

\frac{d}{d x} (2 3 x^{7})

\frac{14 x ^{\frac{4}{3}}}{3}

Schritte zur Lösung

\frac{d}{d x} (2 3 x^{7})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (3 x^{7})

Wende die Kettenregel an:

\frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{7})

= \frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{7})

\frac{d}{d x} (x^{7}) = 7 x^{6}

= 2 \cdot \frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \cdot 7 x^{6}

Vereinfache

2 \cdot \frac{1}{3 ( x ^{7} ) ^{\frac{2}{3}}} \cdot 7 x^{6} : \frac{14 x ^{\frac{4}{3}}}{3}

= \frac{14 x ^{\frac{4}{3}}}{3}

\int x^{2} - 8 x + 12 d x

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