derivative of \sqrt[3]{2x-x^2}

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e 4 x e^{- k x}

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