Question

What is the derivative of `f(x)=tan^-1(e^x)` ?

Answer 1

By Chain Rule, 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}}`