# Differentiate <sp

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,

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