derivative of 3/(5x^{2/5})

Lösung

\frac{d}{d x} (\frac{3}{5 x ^{\frac{2}{5}}})

- \frac{6}{25 x ^{\frac{7}{5}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3}{5 x ^{\frac{2}{5}}})

Entferne die Konstante:

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

= \frac{3}{5} \frac{d}{d x} (\frac{1}{x ^{\frac{2}{5}}})

Wende Exponentenregel an:

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

= \frac{3}{5} \frac{d}{d x} (x^{- \frac{2}{5}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{3}{5} (- \frac{2}{5} x^{- \frac{2}{5} - 1})

Vereinfache

\frac{3}{5} (- \frac{2}{5} x^{- \frac{2}{5} - 1}) : - \frac{6}{25 x ^{\frac{7}{5}}}

= - \frac{6}{25 x ^{\frac{7}{5}}}

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