Answer
$$\frac{{dy}}{{dx}} = - 12{e^{2x}}$$
Work Step by Step
$$\eqalign{
& y = - 6{e^{2x}} \cr
& {\text{differentiate both sides}} \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ { - 6{e^{2x}}} \right] \cr
& \frac{{dy}}{{dx}} = - 6\frac{d}{{dx}}\left[ {{e^{2x}}} \right] \cr
& {\text{use }}\frac{d}{{dx}}\left[ {{e^{ax}}} \right] = a{e^{ax}} \cr
& \frac{{dy}}{{dx}} = - 6\left( {2{e^{2x}}} \right) \cr
& \frac{{dy}}{{dx}} = - 12{e^{2x}} \cr} $$