Answer
$f(x)$ is differentiable $\forall x\in\mathbb{R}-\{3\}$.
Work Step by Step
Step-1: Differentiate the following equation,
$$f(x)=(x-3)^{2/5}$$,
$$f'(x)=\frac{2}{5}\times \frac{1}{(x-3)^{3/5}}$$
Step-2: It can be clearly seen that $f'(x)$ is not defined at $x=3$. Thus, $f(x)$ is differentiable at all values of $x$ except $3$.
