Answer
$$dy = \left( {3 - \sin 2x} \right)dx$$
Work Step by Step
$$\eqalign{
& y = 3x - {\sin ^2}x \cr
& {\text{Differentiate both sides with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {3x - {{\sin }^2}x} \right] \cr
& \frac{{dy}}{{dx}} = 3 - 2\sin x\frac{d}{{dx}}\left[ {\sin x} \right] \cr
& \frac{{dy}}{{dx}} = 3 - 2\sin x\left( {\cos x} \right) \cr
& \frac{{dy}}{{dx}} = 3 - 2\sin x\cos x \cr
& {\text{Recall that }}\sin 2x = 2\sin x\cos x \cr
& \frac{{dy}}{{dx}} = 3 - \sin 2x \cr
& {\text{Write in differential form }}dy = f'\left( x \right)dx \cr
& dy = \left( {3 - \sin 2x} \right)dx \cr} $$
