I have checked not few books in regard to directional derivatives. Practically all of them use vectors in the derivative definition. I would like to read a good explanation of this concept but keeping out the geometrical interpretations. Suppose we got a function of two variables. I understand that a directional derivative has to do with increments of the two variables. Would someone mind explain how to build this concept employing only analytical concepts, without turning to directions in a plane? Or maybe my wish is a nonsense ?