Let and.

We need to differentiate u with respect to v that is find.

We have

By substituting ax = sin θ, we have

[∵ sin²θ + cos²θ = 1]

⇒ u = sin^–1(2sinθcosθ)

⇒ u = sin^–1(sin2θ)

Given

However, ax = sin θ

Hence, u = sin^–1(sin 2θ) = 2θ.

⇒ u = 2sin^–1(ax)

On differentiating u with respect to x, we get

We know

We know

Now, we have

On differentiating v with respect to x, we get

We know

We know and derivative of a constant is 0.

We have

Thus,