# How do you differentiate x^(2/3)+y^(2/3)=4?

In this case of implicit differentiation consider that $y$ is function of $x$ so you get:
$\frac{2}{3} {x}^{\frac{2}{3} - 1} + \frac{2}{3} {y}^{\frac{2}{3} - 1} \frac{\mathrm{dy}}{\mathrm{dx}} = 0$
$\frac{\mathrm{dy}}{\mathrm{dx}} = - \frac{{x}^{- \frac{1}{3}}}{{y}^{- \frac{1}{3}}} = - \sqrt[3]{\frac{y}{x}}$
Where $y = {\left(4 - {x}^{\frac{2}{3}}\right)}^{\frac{3}{2}}$ from your original expression.