derivative f(x)=(2-3x^3)^{-2}

Lösung

ableitung von

f (x) = (2 - 3 x^{3})^{- 2}

\frac{18 x ^{2}}{( 2 - 3 x ^{3} ) ^{3}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{2}{( 2 - 3 x ^{3} ) ^{3}} (- 9 x^{2}) : \frac{18 x ^{2}}{( 2 - 3 x ^{3} ) ^{3}}

= \frac{18 x ^{2}}{( 2 - 3 x ^{3} ) ^{3}}

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