1. The problem statement, all variables and given/known data Given an interval I. The function f goes from I to the real line. Define f as f(x)=x^2 if x rational or 0 if x is irrational. show that f i differentiablle at x=0 and find its derivative at this point, i.e. x=0. 2. Relevant equations I have a given lead on this. That |f(x)/x|<|x|. But I'm not sure how this should help me. I have started with the definition and I have tried to determine a certain epsilon for which this is true. But I don't know how. 3. The attempt at a solution I have shown that the function is continuous at this point and therefore know that the derivative might exist. But when it comes to the actual differentiability I have that (according to the definition), given a positive epsilon there exists a delta. For x satisfying the inequality 0<|x-c|<delta, the inequality |(f(x)-f(c))/(x-c)-L|<epsilon holds. L then is called f's derivative in the point c. I'm not sure if this counts as an attempt. But this problem is really bugging me. Hopes for an answer!