Answer
$$\frac{{dy}}{{dx}} = - 28\cos 7x$$
Work Step by Step
$$\eqalign{
& y = - 4\sin 7x \cr
& {\text{differentiate with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ { - 4\sin 7x} \right] \cr
& {\text{use multiple constant rule}} \cr
& \frac{{dy}}{{dx}} = - 4\frac{d}{{dx}}\left[ {\sin 7x} \right] \cr
& {\text{using the chain rule for }}{D_x}\left( {\sin u} \right) = \cos u \cdot {D_x}\left( u \right).{\text{ then}} \cr
& \frac{{dy}}{{dx}} = - 4\left( {\cos 7x} \right)\frac{d}{{dx}}\left[ {7x} \right] \cr
& \frac{{dy}}{{dx}} = - 4\left( {\cos 7x} \right)\left( 7 \right) \cr
& {\text{simplifying}} \cr
& \frac{{dy}}{{dx}} = - 28\cos 7x \cr} $$
