derivative of \sqrt[5]{x^2}

Lösung

\frac{d}{d x} (5 x^{2})

\frac{2}{5 x ^{\frac{3}{5}}}

Schritte zur Lösung

\frac{d}{d x} (5 x^{2})

Wende die Kettenregel an:

\frac{1}{5 ( x ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{2})

= \frac{1}{5 ( x ^{2} ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{2})

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

= \frac{1}{5 ( x ^{2} ) ^{\frac{4}{5}}} \cdot 2 x

Vereinfache

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

= \frac{2}{5 x ^{\frac{3}{5}}}

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