Question

How do you find the derivative of `(arcsin(x))^(2)`?

Answer 1

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

Explanation:

Use the Chain Rule.

`frac{d}{dx}((sin^{-1}x)^2) = 2*sin^{-1}x*frac{d}{dx}(sin^{-1}x)`

`= 2*sin^{-1}x*frac{1}{sqrt{1-x^2}`