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