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Beliebt Rechnen >

derivative (1+x^4)^{2/3}

Lösung

ableitung von

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

Lösung

\frac{8 x ^{3}}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{8 x ^{3}}{3 ( 1 + x ^{4} ) ^{\frac{1}{3}}}

Graph

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