So, it is the "f" in (5) that you want to prove differentiable and not F?

Do you recall thedefinitionof "differentiable" for a function of two variables?

f(x, y) is differentiable at if and only if there exist a linear function L(x,y)= ax+ by and a function such that

1) and

2)

The demominator in (2) can be replaced with any reasonable measure of "distance" from