derivative of arcsin(10x)

解答

\frac{d}{d x} (arcsin (10 x))

\frac{10}{1 - 100 x ^{2}}

求解步骤

\frac{d}{d x} (arcsin (10 x))

使用连锁律:

\frac{1}{1 - ( 10 x ) ^{2}} \frac{d}{d x} (10 x)

= \frac{1}{1 - ( 10 x ) ^{2}} \frac{d}{d x} (10 x)

\frac{d}{d x} (10 x) = 10

= \frac{1}{1 - ( 10 x ) ^{2}} \cdot 10

化简

\frac{1}{1 - ( 10 x ) ^{2}} \cdot 10 : \frac{10}{1 - 100 x ^{2}}

= \frac{10}{1 - 100 x ^{2}}

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