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Beliebt Rechnen >

derivative \sqrt[5]{2x^3+8x}

Lösung

ableitung von

5 2 x^{3} + 8 x

Lösung

\frac{6 x ^{2} + 8}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

Schritte zur Lösung

\frac{d}{d x} (5 2 x^{3} + 8 x)

Wende die Kettenregel an:

\frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} \frac{d}{d x} (2 x^{3} + 8 x)

= \frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} \frac{d}{d x} (2 x^{3} + 8 x)

\frac{d}{d x} (2 x^{3} + 8 x) = 6 x^{2} + 8

= \frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} (6 x^{2} + 8)

Vereinfache

\frac{1}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}} (6 x^{2} + 8) : \frac{6 x ^{2} + 8}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

= \frac{6 x ^{2} + 8}{5 ( 2 x ^{3} + 8 x ) ^{\frac{4}{5}}}

Graph

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