How do you find the derivative of ${(arcsin (x))}^{2}$ $(arcsin(x))^(2)$ ?

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How do you find the derivative of ${(arcsin (x))}^{2}$ $(arcsin(x))^(2)$ ?

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Answer 1 · 2016-02-14T03:05:34

$\frac{d}{d x} ({({sin}^{- 1} x)}^{2}) = \frac{2 {sin}^{- 1} x}{\sqrt{1 - x^{2}}}$ $frac{d}{dx}((sin^{-1}x)^2) = frac{2sin^{-1}x}{sqrt{1-x^2}$

Explanation:

Use the Chain Rule.

$\frac{d}{d x} ({({sin}^{- 1} x)}^{2}) = 2 \cdot {sin}^{- 1} x \cdot \frac{d}{d x} ({sin}^{- 1} x)$ $frac{d}{dx}((sin^{-1}x)^2) = 2*sin^{-1}x*frac{d}{dx}(sin^{-1}x)$

$= 2 \cdot {sin}^{- 1} x \cdot \frac{1}{\sqrt{1 - x^{2}}}$ $= 2*sin^{-1}x*frac{1}{sqrt{1-x^2}$

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How do you find the derivative of ${(arcsin (x))}^{2}$ $(arcsin(x))^(2)$ ?

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