derivative cos(arcsin(x))

解

導関数

cos (arcsin (x))

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

解答ステップ

\frac{d}{d x} (cos (arcsin (x)))

簡素化

cos (arcsin (x)) : 1 - x^{2}

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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