Let and v = cos^–1x.

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

We have

By substituting x = cos θ, we have

[∵ sin²θ + cos²θ = 1]

⇒ u = sin^–1(sin θ)

(i) Given x ϵ (0, 1)

However, x = cos θ.

⇒ cos θ ϵ (0, 1)

Hence, u = sin^–1(sin θ) = θ.

⇒ u = cos^–1x

On differentiating u with respect to x, we get

We know

Now, on differentiating v with respect to x, we get

We have,

Thus,