derivative of sqrt(1/(x^{27)})

解

\frac{d}{d x} (\frac{1}{x ^{27}})

- \frac{27}{2 x ^{\frac{29}{2}}}

解答ステップ

\frac{d}{d x} (\frac{1}{x ^{27}})

連鎖法則を適用:

\frac{1}{2 \frac{1}{x ^{27}}} \frac{d}{d x} (\frac{1}{x ^{27}})

= \frac{1}{2 \frac{1}{x ^{27}}} \frac{d}{d x} (\frac{1}{x ^{27}})

\frac{d}{d x} (\frac{1}{x ^{27}}) = - \frac{27}{x ^{28}}

= \frac{1}{2 \frac{1}{x ^{27}}} (- \frac{27}{x ^{28}})

簡素化

\frac{1}{2 \frac{1}{x ^{27}}} (- \frac{27}{x ^{28}}) : - \frac{27}{2 x ^{\frac{29}{2}}}

= - \frac{27}{2 x ^{\frac{29}{2}}}