Answer
$$\frac{{dy}}{{dx}} = 4{e^{0.5x}}$$
Work Step by Step
$$\eqalign{
& y = 8{e^{0.5x}} \cr
& {\text{differentiate both sides}} \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {8{e^{0.5x}}} \right] \cr
& \frac{{dy}}{{dx}} = 8\frac{d}{{dx}}\left[ {{e^{0.5x}}} \right] \cr
& \frac{{dy}}{{dx}} = 8\left( {0.5{e^{0.5x}}} \right) \cr
& \frac{{dy}}{{dx}} = 4{e^{0.5x}} \cr} $$
