Answer
Does not exist.
Work Step by Step
$f(x)=(x-6)^{\frac{2}{3}}$
$f'(c)=\lim\limits_{x \to c}\frac{f(x)-f(c)}{x-c}$
$f'(6)=\lim\limits_{x \to 6}\frac{(x-6)^{\frac{2}{3}}-((6)-6)^{\frac{2}{3}}}{x-6}$
$f'(6)=\lim\limits_{x \to 6}\frac{(x-6)^{\frac{2}{3}}}{x-6}$
$f'(6)=\lim\limits_{x \to 6}\frac{1}{\sqrt[3] {x-6}}$
$f'(6)=\frac{1}{\sqrt[3] {(6)-6}}$
$f'(6)=\frac{1}{0}$
Does not exist.
