Differentiate with respect to if –1 < x < 1.

Let and

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

We have

By substituting x = tan θ, we have

Given, –1 < x < 1 ⇒ x ϵ (–1, 1)

However, x = tan θ

⇒ tan θ ϵ (–1, 1)

Hence,

On differentiating u with respect to x, we get

We know and derivative of a constant is 0.

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,