derivative of (x^3-9x^{-1/3})

Lösung

\frac{d}{d x} ((x^{3} - 9 x)^{- \frac{1}{3}})

- \frac{x ^{2} - 3}{( x ^{3} - 9 x ) ^{\frac{4}{3}}}

Schritte zur Lösung

\frac{d}{d x} ((x^{3} - 9 x)^{- \frac{1}{3}})

Wende die Kettenregel an:

- \frac{1}{3 ( x ^{3} - 9 x ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{3} - 9 x)

= - \frac{1}{3 ( x ^{3} - 9 x ) ^{\frac{4}{3}}} \frac{d}{d x} (x^{3} - 9 x)

\frac{d}{d x} (x^{3} - 9 x) = 3 x^{2} - 9

= - \frac{1}{3 ( x ^{3} - 9 x ) ^{\frac{4}{3}}} (3 x^{2} - 9)

Vereinfache

- \frac{1}{3 ( x ^{3} - 9 x ) ^{\frac{4}{3}}} (3 x^{2} - 9) : - \frac{x ^{2} - 3}{( x ^{3} - 9 x ) ^{\frac{4}{3}}}

= - \frac{x ^{2} - 3}{( x ^{3} - 9 x ) ^{\frac{4}{3}}}

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