What is $\frac{d}{dx}\left(\tan^{-1}{\left(e^{x} \right)}\right)$?

Explanation

1. 01

   With $u = e^{x}$, $u' = e^{x}$ and $u^{2} = e^{2x}$.

2. 02

   $\frac{e^{x}}{1 + e^{2x}}$.