It asks you to prove that the derivative of f(x,y) in (0,0) in the direction of a generic vectorv(directional derivative)exists.You can do this thinking of v as (a,b) for example, or (cos , sin ).

Then you have to prove that f(x,y) is not differentiable at that point.

Do you understand why this would be "surprising" as the exercise says, and what two important concepts is it referring to?