Given x ϵ (–1, 0)

However, x = cos θ.

⇒ cos θ ϵ (–1, 0)

Hence, u = sin^–1(sin θ) = π – θ.

⇒ u = π – cos^–1x

On differentiating u with respect to x, we get

We know and derivative of a constant is 0.

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

We have

Thus,