Differentiate log(1 + x 2 ) with respect to tan –1 x.

Question

Philoid · Accepted Answer

Let u = log(1 + x²) and v = tan^–1x.

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

On differentiating u with respect to x, we get

We know

[using chain rule]

However, and derivative of a constant is 0.

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

We know

We have

Thus,