#### Answer

$\dfrac {\cos \sqrt {x}}{4\sqrt {x\sin \sqrt {x}}}$

#### Work Step by Step

$\dfrac {d}{dx}\left( \sqrt {\sin \sqrt {x}}\right) =\dfrac {1}{2}\times \left( \sin \sqrt {x}\right) ^{\dfrac {1}{2}-1}\times \left( \dfrac {d}{dx}\sin \sqrt {x}\right) =\dfrac {1}{2\sqrt {\sin \sqrt {x}}}\times \cos \sqrt {x}\times \left( \dfrac {d}{dx}\sqrt {x}\right) =\dfrac {\cos \sqrt {x}}{4\sqrt {x\sin \sqrt {x}}}$