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Beliebt Rechnen >

derivative of 2/(\sqrt[3]{x^2})

Lösung

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

Lösung

- \frac{4}{3 x ^{\frac{5}{3}}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

2 (- \frac{1}{3 ( x ^{2} ) ^{\frac{4}{3}}} \cdot 2 x) : - \frac{4}{3 x ^{\frac{5}{3}}}

= - \frac{4}{3 x ^{\frac{5}{3}}}

Graph

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