derivative of \sqrt[5]{ln(7-x^2})

解

\frac{d}{d x} (5 ln (7 - x^{2}))

- \frac{2 x}{5 ln ^{\frac{4}{5}} ( 7 - x ^{2} ) ( 7 - x ^{2} )}

解答ステップ

\frac{d}{d x} (5 ln (7 - x^{2}))

連鎖法則を適用:

\frac{1}{5 ( ln ( 7 - x ^{2} ) ) ^{\frac{4}{5}}} \frac{d}{d x} (ln (7 - x^{2}))

= \frac{1}{5 ( ln ( 7 - x ^{2} ) ) ^{\frac{4}{5}}} \frac{d}{d x} (ln (7 - x^{2}))

\frac{d}{d x} (ln (7 - x^{2})) = - \frac{2 x}{7 - x ^{2}}

= \frac{1}{5 ( ln ( 7 - x ^{2} ) ) ^{\frac{4}{5}}} (- \frac{2 x}{7 - x ^{2}})

簡素化

\frac{1}{5 ln ^{\frac{4}{5}} ( 7 - x ^{2} )} (- \frac{2 x}{7 - x ^{2}}) : - \frac{2 x}{5 ln ^{\frac{4}{5}} ( 7 - x ^{2} ) ( 7 - x ^{2} )}

= - \frac{2 x}{5 ln ^{\frac{4}{5}} ( 7 - x ^{2} ) ( 7 - x ^{2} )}