Can you help me find if this function is differentiable?
$$f(x,y)={\sqrt{\frac{7}{1+|ln(x^2+y^2-2x-2y|}-\frac{1}{10}}}$$
I found domain. And I found partial derivatives (same domain). But I don't know how to prove if function is differentiable or not in general. If partial derivatives are continuous functions and have same domain as original function, does that mean function is differentiable on its domain?