Differentiate `sin(m\ sin^(-1)x)` with respect to `x` :

Explanation

Given that,

`y=sin(m\ sin^(-1)x)`

`frac{dy}{dx}=y'=frac{d}{dx}sin(m\ sin^(-1)x)`

`frac{dy}{dx}=cos(m\ sin^(-1)x) times m times frac{1}{sqrt(1-x^2)}`

`frac{dy}{dx}=frac{m cos(m\ sin^(-1)x)}{sqrt(1-x^2)} `


Answer is:

`frac{dy}{dx}=frac{m cos(m\ sin^(-1)x)}{sqrt(1-x^2)} `