derivative y=ln(sqrt(1-x^2))

解

導関数

y = ln (1 - x^{2})

- \frac{x}{1 - x ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{x}{1 - x ^{2}}