I was reviewing basic calculus of of functions of several variables. It struck me that in one of the exercises, it was required to show that a given function has directional derivative for all directions at the origin (0,0) even though it is not continuous at (0,0). Without getting into the details , I thought that this does not make sense as the function has to be differentiable at (0,0) for the directional derivatives to exist. And differentiability implies the continuity of the function at (0,0). Am I missing something here?