Answer
$$\frac{{dy}}{{dx}} = 56x\sin \left( {7{x^2} - 4} \right)$$
Work Step by Step
$$\eqalign{
& y = - 4\cos \left( {7{x^2} - 4} \right) \cr
& {\text{differentiate with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ { - 4\cos \left( {7{x^2} - 4} \right)} \right] \cr
& {\text{use multiple constant rule}} \cr
& \frac{{dy}}{{dx}} = - 4\frac{d}{{dx}}\left[ {\cos \left( {7{x^2} - 4} \right)} \right] \cr
& {\text{using the chain rule for }}{D_x}\left( {\tan u} \right) = {\sec ^2}u \cdot {D_x}\left( u \right).{\text{ consider }}u = 9x + 1 \cr
& \frac{{dy}}{{dx}} = - 4\left( { - \sin \left( {7{x^2} - 4} \right)} \right)\frac{d}{{dx}}\left[ {7{x^2} - 4} \right] \cr
& {\text{then}} \cr
& \frac{{dy}}{{dx}} = 4\sin \left( {7{x^2} - 4} \right)\left( {14x} \right) \cr
& {\text{simplifying}} \cr
& \frac{{dy}}{{dx}} = 56x\sin \left( {7{x^2} - 4} \right) \cr} $$
