1. The problem statement, all variables and given/known data f:R->R is defined as f(x) when x[itex]\neq 0[/itex], and 1 when x=0. Find f'(0). 2. Relevant equations 3. The attempt at a solution Since I can prove that f is continuous at x=0, does that allow me to take the the limit of f'(x) as x-> 0, which is 0? It is quite easy to see that the correct answer must be f'(0)=0, but do i break any rules if I first differentiate f(x) and then look at the limit as x-> 0? Thanks!