Answer
$y'=\frac{4}{3}\sqrt[3] x+\frac{2}{3}x^{-2/3}$
Work Step by Step
$y=\sqrt[3] x(2+x)$
Use the product rule.
$y'=\sqrt[3] x(1)+(2+x)(\frac{1}{3}x^{-2/3})$
Clean up and simplify.
$y'=\sqrt[3] x+\frac{2}{3}x^{-2/3}+\frac{1}{3}\sqrt[3] x$
$y'=\frac{4}{3}\sqrt[3] x+\frac{2}{3}x^{-2/3}$