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Beliebt Rechnen >

derivative of \sqrt[3]{8x^7+9x^6}

Lösung

Lösung

\frac{2 x ( 28 x + 27 )}{3 ( 8 x + 9 ) ^{\frac{2}{3}}}

Schritte zur Lösung

Wende die Kettenregel an:

\frac{1}{3 ( 8 x ^{7} + 9 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (8 x^{7} + 9 x^{6})

= \frac{1}{3 ( 8 x ^{7} + 9 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (8 x^{7} + 9 x^{6})

\frac{d}{d x} (8 x^{7} + 9 x^{6}) = 56 x^{6} + 54 x^{5}

= \frac{1}{3 ( 8 x ^{7} + 9 x ^{6} ) ^{\frac{2}{3}}} (56 x^{6} + 54 x^{5})

Vereinfache

\frac{1}{3 ( 8 x ^{7} + 9 x ^{6} ) ^{\frac{2}{3}}} (56 x^{6} + 54 x^{5}) : \frac{2 x ( 28 x + 27 )}{3 ( 8 x + 9 ) ^{\frac{2}{3}}}

= \frac{2 x ( 28 x + 27 )}{3 ( 8 x + 9 ) ^{\frac{2}{3}}}

Graph

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