Given that y=sin^-1(3x-4x³)

Let x=sin θ

⇒ θ=sin^-1x

Then, y= sin^-1(3sinθ -4sin³θ)

Using sin3θ=3sinθ -4sin³θ, we get

y=sin^-1(sin3θ)=3θ=3sin^-1x

Differentiating with respect to x, we get