$\displaystyle f(x) = \left\{ {\begin{array}{rl} {0,} & {x \in \mathbb{Q}} \\ {x^2 - x^4 ,} & {x \notin \mathbb{Q}} \\ \end{array} } \right.$

I'm trying to find $\displaystyle f'(x)$. I think the function f is not continuous except at points 0 and 1. So if I can show that, that means f is not differentiable except (possibly) at 0 and 1. Am I going in the right direction?

If so, then f'(0) would be 0, but I'm not sure about f'(1)...