Showing differentiability in R^n

[precondition]

When you are given a function and asked for differentiability at a point in domain or the whole domain, what's the normal procedure? I think the definition is almost useless in here...
Also, I'm still stuck on the previous questions so if anyone bothers to check them out...

 

[AKG]

The definition is entirely useful, and the previous question has already been answered.