Answer
The derivative does not exist at c=0.
Work Step by Step
The derivative of $ f(x) = x^\frac{2}{3}$ is $f'(x) = \frac{2}{3}x^\frac{-1}{3}$, or $\frac{2}{3x^\frac{1}{3}} $
$f'(x)$ is invalid when the denominator is 0. This occurs at the point x (or c) = 0.
