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Beliebt Rechnen >

derivative of \sqrt[9]{x^8}

Lösung

\frac{d}{d x} (9 x^{8})

Lösung

\frac{8}{9 x ^{\frac{1}{9}}}

Schritte zur Lösung

\frac{d}{d x} (9 x^{8})

Wende die Kettenregel an:

\frac{1}{9 ( x ^{8} ) ^{\frac{8}{9}}} \frac{d}{d x} (x^{8})

= \frac{1}{9 ( x ^{8} ) ^{\frac{8}{9}}} \frac{d}{d x} (x^{8})

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

= \frac{1}{9 ( x ^{8} ) ^{\frac{8}{9}}} \cdot 8 x^{7}

Vereinfache

\frac{1}{9 ( x ^{8} ) ^{\frac{8}{9}}} \cdot 8 x^{7} : \frac{8}{9 x ^{\frac{1}{9}}}

= \frac{8}{9 x ^{\frac{1}{9}}}

Graph

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