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

Lösung

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

\frac{4}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{4}{3 x ^{\frac{1}{3}}}

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