Differentiate `(a^(sin^(-1)x))^2` with respect to `x` :

Explanation

Let `y=(a^(sin^(-1)x))^2`

We know that,

`y=a^x`

`y'=a^x * loga`


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

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

`frac{dy}{dx}= frac{x(a^(sin^(-1)x))^2* log a * 2sin^(-1)x}{sqrt(1-x^2)}`