Let U={(x,y) in R2:x2+y2<4}, and let f(x,y)=√.(4−x2−y2)
Prove that f is differentiable, and find its derivative.

I do know how to prove it is differentiable at a specific point in R2, but I could not generalize it to prove it differentiable on R2. Any hint?

I think that they want you to prove that f(x,y) is differentiable on U, as it is not well-defined on all of R2. For example, what is f(3,4)?