derivative of arccos(arcsin(x))

解答

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

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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

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