Answer
$\dfrac {\cos \sqrt {x}}{2\sqrt {x}}-\dfrac {\sin \sqrt {x}}{2}$
Work Step by Step
$\dfrac {d}{dx}\left( \sqrt {x}\cos \left( \sqrt {x}\right) \right) =\left( \dfrac {d}{dx}\left( \sqrt {x}\right) \right) \times \cos \sqrt {x}+\left( \dfrac {d}{dx}\left( \cos \sqrt {x}\right) \right) \times \sqrt {x}=\dfrac {\cos \sqrt {x}}{2\sqrt {x}}-\left( \sin \sqrt {x}\right) \times \sqrt {x}\times \left( \dfrac {d}{dx}\sqrt {x}\right) =\dfrac {\cos \sqrt {x}}{2\sqrt {x}}-\dfrac {\sin \sqrt {x}}{2}$
