Where is this function differentiable?

[Omega017]

How do I go about determining where $$f(x,y) = \sqrt{|x| + |y|}$$ is differentiable?

 

[slider142]

A function is differentiable at a point if the function's partial derivatives exist and are continuous at that point. First, find the function's partial derivatives. The function is differentiable at all points where the partial derivatives are continuous.
For the points where the function's partial derivatives are not continuous, you will have to manually test the differentiability of the function using the definition of the derivative. However, for this particular function, a quick look at the cross-sections should let you know.