Answer
$$\frac{{dy}}{{dx}} = 10x{e^{2x}} + 5{e^{2x}}$$
Work Step by Step
$$\eqalign{
& y = 5x{e^{2x}} \cr
& {\text{differentiate both sides}} \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {5x{e^{2x}}} \right] \cr
& {\text{use product rule}} \cr
& \frac{{dy}}{{dx}} = 5x\frac{d}{{dx}}\left[ {{e^{2x}}} \right] + {e^{2x}}\frac{d}{{dx}}\left[ {5x} \right] \cr
& {\text{find derivatives}} \cr
& \frac{{dy}}{{dx}} = 5x\left( {2{e^{2x}}} \right) + {e^{2x}}\left( 5 \right) \cr
& {\text{Simplify}} \cr
& \frac{{dy}}{{dx}} = 10x{e^{2x}} + 5{e^{2x}} \cr} $$