Answer
$$\frac{{dy}}{{dx}} = \frac{2}{3}{e^{2x/3}}$$
Work Step by Step
$$\eqalign{
& y = {e^{2x/3}} \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {{e^{2x/3}}} \right] \cr
& {\text{We can use the formula }}\frac{d}{{dx}}{e^u} = {e^u}\frac{{du}}{{dx}}{\text{ where }}u{\text{ is any differentiable function of }}x. \cr
& {\text{For this exercise you can note that }}u = \frac{{2x}}{3},{\text{ then}} \cr
& \frac{{dy}}{{dx}} = {e^{2x/3}}\frac{d}{{dx}}\left[ {\frac{{2x}}{3}} \right] \cr
& {\text{solve the derivative and simplify}} \cr
& \frac{{dy}}{{dx}} = {e^{2x/3}}\left( {\frac{2}{3}} \right) \cr
& \frac{{dy}}{{dx}} = \frac{2}{3}{e^{2x/3}} \cr} $$
