Total Derivative vs. Directional Derivative
I am having a little difficulty in understanding the following problem. I present it with some thoughts:
2) Give an example of a function f:R2 --> R that has directional derivatives in every direction but that is not differentiable. Explain why your example works.
I understand the difference between a directional derivative and a total derivative, but I can't think of any examples where the directional derivatives in all directions are well-defined and the total derivative isn't. In order for f to be totally differentiable at (x,y), the partials of f w.r.t. (x,y) must be defined and continuous. It seems that total differentiability is stronger than directional differentiability, I just can't think of any examples that show that.