derivative of sqrt(1/(x^{25)})

Lösung

\frac{d}{d x} (\frac{1}{x ^{25}})

- \frac{25}{2 x ^{\frac{27}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ^{25}})

Wende die Kettenregel an:

\frac{1}{2 \frac{1}{x ^{25}}} \frac{d}{d x} (\frac{1}{x ^{25}})

= \frac{1}{2 \frac{1}{x ^{25}}} \frac{d}{d x} (\frac{1}{x ^{25}})

\frac{d}{d x} (\frac{1}{x ^{25}}) = - \frac{25}{x ^{26}}

= \frac{1}{2 \frac{1}{x ^{25}}} (- \frac{25}{x ^{26}})

Vereinfache

\frac{1}{2 \frac{1}{x ^{25}}} (- \frac{25}{x ^{26}}) : - \frac{25}{2 x ^{\frac{27}{2}}}

= - \frac{25}{2 x ^{\frac{27}{2}}}

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