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Beliebt Rechnen >

derivative of \sqrt[5]{x^8}

Lösung

\frac{d}{d x} (5 x^{8})

Lösung

\frac{8 x ^{\frac{3}{5}}}{5}

Schritte zur Lösung

\frac{d}{d x} (5 x^{8})

Wende die Kettenregel an:

\frac{1}{5 ( x ^{8} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{8})

= \frac{1}{5 ( x ^{8} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{1}{5 ( x ^{8} ) ^{\frac{4}{5}}} \cdot 8 x^{7}

Vereinfache

\frac{1}{5 ( x ^{8} ) ^{\frac{4}{5}}} \cdot 8 x^{7} : \frac{8 x ^{\frac{3}{5}}}{5}

= \frac{8 x ^{\frac{3}{5}}}{5}

Graph

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