Answer
$$\frac{{dy}}{{dx}} = - 7{e^{5 - 7x}}$$
Work Step by Step
$$\eqalign{
& y = {e^{5 - 7x}} \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {{e^{5 - 7x}}} \right] \cr
& {\text{We can use the formula }}\frac{d}{{dx}}{e^u} = {e^u}\frac{{du}}{{dx}};{\text{ where }}u{\text{ is any differentiable function of }}x \cr
& {\text{for this exercise you can note that }}u = 5 - 7x,{\text{ then}} \cr
& \frac{{dy}}{{dx}} = {e^{5 - 7x}}\frac{d}{{dx}}\left[ {5 - 7x} \right] \cr
& {\text{solve the derivative and simplify}} \cr
& \frac{{dy}}{{dx}} = {e^{5 - 7x}}\left( { - 7} \right) \cr
& \frac{{dy}}{{dx}} = - 7{e^{5 - 7x}} \cr} $$
