Question

d/dx {tan^-1(e^x)} is equal is

Answer 1

Hello User,

QUESTION ⬇️

d/dx {tan^-1(e^x)} is equal is?

ANSWER ⬇️

we can find #f'(x)=frac{e^x}{1+e^{2x}}#.

Note: #[tan^{-1}(x)]'={1}/{1+x^2}#.

By Chain Rule,

#f'(x)={1}/{1+(e^x)^2}cdot e^x={e^x}/{1+e^{2x}}#