Answer
$\dfrac {1}{2\left( 1+x^{2}\right) \sqrt {\arctan x}}$
Work Step by Step
$\dfrac {d}{dx}\sqrt {\arctan x}=\dfrac {1}{2}\dfrac {1}{\sqrt {\arctan x}}\times \left( \dfrac {d}{dx}\left( \arctan x\right) \right) =\dfrac {1}{2\left( 1+x^{2}\right) \sqrt {\arctan x}}$
