#### Answer

$\frac{dy}{dx} = \frac{2}{3}e^{\frac{2x}{3}}$

#### Work Step by Step

$y = u^{\frac{2}{3}}$
where,
$u = e^{x}$
Now,
$\frac{dy}{du} = \frac{2}{3}u^{-\frac{1}{3}}$
and,
$\frac{du}{dx} = e^{x}$
So,
$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$
$\frac{dy}{dx} = \frac{2}{3}u^{-\frac{1}{3}} \times e^{x}$
$\frac{dy}{dx} = \frac{2}{3}e^{-\frac{1x}{3}} \times e^{x}$
$\frac{dy}{dx} = \frac{2}{3}e^{\frac{2x}{3}}$