derivative of (arcsin(2x)^2)

解

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

\frac{4 arcsin ( 2 x )}{1 - 4 x ^{2}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (arcsin (2 x)) = \frac{2}{1 - 4 x ^{2}}

= 2 arcsin (2 x) \frac{2}{1 - 4 x ^{2}}

簡素化

2 arcsin (2 x) \frac{2}{1 - 4 x ^{2}} : \frac{4 arcsin ( 2 x )}{1 - 4 x ^{2}}

= \frac{4 arcsin ( 2 x )}{1 - 4 x ^{2}}