Differentiate with respect to sec^–1 x.

Let and v = sec^–1x

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

We have

But, cos2θ = cos²θ – sin²θ and sin2θ = 2sinθcosθ.

[∵ sin²θ + cos²θ = 1]

Dividing the numerator and denominator with, we get

On differentiating u with respect to x, we get

We know and derivative of a constant is 0.

Now, we have v = sec^–1x

On differentiating v with respect to x, we get

We know

We have

Thus,