(ln(1-x^2))^'

解

(ln (1 - x^{2}))^{^{'}}

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

解答ステップ

(ln (1 - x^{2}))^{'}

連鎖法則を適用:

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

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

(1 - x^{2})^{'} = - 2 x

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

簡素化

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

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