Given that y=cos^-1(4x³-3x)

Let x=cos θ

⇒ θ=cos^-1x

Then, y=cos^-1(4cos³θ-3cosθ)

Using cos3θ=4cos³θ-3cosθ , we get

y=cos^-1(cos3θ)=3=3cos^-1x

Differentiating with respect to x, we get