Answer
$$\frac{{dy}}{{dx}} = - 5{e^{ - 5x}}$$
Work Step by Step
$$\eqalign{
& y = {e^{ - 5x}} \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {{e^{ - 5x}}} \right] \cr
& {\text{we can use the formula }}\frac{d}{{dx}}{e^u} = {e^u}\frac{{du}}{{dx}}{\text{ where }}u{\text{ is any differentiable function of }}x. \cr
& {\text{For this exercise you can note that }}u = - 5x,{\text{ then}} \cr
& \frac{{dy}}{{dx}} = {e^{ - 5x}}\frac{d}{{dx}}\left[ { - 5x} \right] \cr
& {\text{solve the derivative and simplify}} \cr
& \frac{{dy}}{{dx}} = {e^{ - 5x}}\left( { - 5} \right) \cr
& \frac{{dy}}{{dx}} = - 5{e^{ - 5x}} \cr} $$
