1. The problem statement, all variables and given/known data Does the function f(x,y) has any partial derivatives? f(x,y) = (x^2 + y^2)^2, if both x and y are rational = 0 , otherwise 2. Relevant equations 3. The attempt at a solution Not sure what to do. I know this function has only one limit at (0,0) and is also continuous there, and nowhere else. So it is not differentiable for (x,y) =/= (0,0). However, this doesn't say anything about existence of the partials. Thanks for any help.