derivative of arcsin^2(x)

解

\frac{d}{d x} (arcsin^{2} (x))

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

解答ステップ

\frac{d}{d x} (arcsin^{2} (x))

連鎖法則を適用:

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

= 2 arcsin (x) \frac{d}{d x} (arcsin (x))

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

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

簡素化

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

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