Answer
$$\frac{{dy}}{{dx}} = 21{x^2}{e^{ - 3x}} - 14x{e^{ - 3x}}$$
Work Step by Step
$$\eqalign{
& y = - 7{x^2}{e^{ - 3x}} \cr
& {\text{differentiate both sides}} \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ { - 7{x^2}{e^{ - 3x}}} \right] \cr
& {\text{use product rule}} \cr
& \frac{{dy}}{{dx}} = - 7{x^2}\frac{d}{{dx}}\left[ {{e^{ - 3x}}} \right] + {e^{ - 3x}}\frac{d}{{dx}}\left[ { - 7{x^2}} \right] \cr
& {\text{find derivatives}} \cr
& \frac{{dy}}{{dx}} = - 7{x^2}\left( { - 3{e^{ - 3x}}} \right) + {e^{ - 3x}}\left( { - 14x} \right) \cr
& {\text{simplify}} \cr
& \frac{{dy}}{{dx}} = 21{x^2}{e^{ - 3x}} - 14x{e^{ - 3x}} \cr} $$
