What is $\frac{d}{dx}\left(\tan^{-1}\sqrt{x}\right)$ for $x > 0$?

Explanation

1. 01

   $\frac{u'}{1 + u^{2}}$ with $u = \sqrt{x}$, $u^{2} = x$ and $u' = \frac{1}{2\sqrt{x}}$.

2. 02

   $\frac{1}{2\sqrt{x}(1 + x)}$.