derivative of 2\sqrt[3]{x^4}

Lösung

\frac{d}{d x} (2 3 x^{4})

\frac{8 x ^{\frac{1}{3}}}{3}

Schritte zur Lösung

\frac{d}{d x} (2 3 x^{4})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (3 x^{4})

Wende die Kettenregel an:

\frac{1}{3 ( x ^{4} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{4})

= \frac{1}{3 ( x ^{4} ) ^{\frac{2}{3}}} \frac{d}{d x} (x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

= 2 \cdot \frac{1}{3 ( x ^{4} ) ^{\frac{2}{3}}} \cdot 4 x^{3}

Vereinfache

2 \cdot \frac{1}{3 ( x ^{4} ) ^{\frac{2}{3}}} \cdot 4 x^{3} : \frac{8 x ^{\frac{1}{3}}}{3}

= \frac{8 x ^{\frac{1}{3}}}{3}

\int 9 sin^{3} (x) cos^{7} (x) d x

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