Answer
$$dy = \frac{{5\cos \left( {5\sqrt x } \right)}}{{2\sqrt x }}dx$$
Work Step by Step
$$\eqalign{
& y = \sin \left( {5\sqrt x } \right) \cr
& {\text{Calculate }}\frac{{dy}}{{dx}} \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {\sin \left( {5\sqrt x } \right)} \right] \cr
& \frac{{dy}}{{dx}} = \cos \left( {5\sqrt x } \right)\frac{d}{{dx}}\left[ {5\sqrt x } \right] \cr
& \frac{{dy}}{{dx}} = \cos \left( {5\sqrt x } \right)\left( {\frac{5}{{2\sqrt x }}} \right) \cr
& \frac{{dy}}{{dx}} = \frac{{5\cos \left( {5\sqrt x } \right)}}{{2\sqrt x }} \cr
& {\text{Write in differential form}} \cr
& dy = \frac{{5\cos \left( {5\sqrt x } \right)}}{{2\sqrt x }}dx \cr} $$
