Define $f:[0,1]\to [0,1]$ by
$f(x)=\begin{cases}0, &x=0,\\ \\ \sum\limits_{r_n
where $\{r_n \}_{n\in \mathbb N} =\mathbb Q \cap (0,1) $.
How to show that the derivative f'(x)=0 a.e.?
I can show this function is increasing and discontinuous at every rational, and how to word on?