$\cos (\sqrt x )$

Let $y = \cos \left( {\sqrt x } \right)$

$\Rightarrow$ $\cfrac{{dy}}{{dx}} = \cfrac{d}{{dx}}\cos \left( {\sqrt x } \right) = - \sin \sqrt x \cdot \cfrac{d}{{dx}}(\sqrt x )$

$= - \sin \sqrt x \cdot \cfrac{1}{2}{(x)^{\cfrac{{ - 1}}{2}}} = \cfrac{{ - \sin \sqrt x }}{{2\sqrt x }}$

therefore $\frac{dy}{dx}=\cfrac{{ - \sin \sqrt x }}{{2\sqrt x }}$