Consider the function $$f(x) = \frac{1}{1-x^2-y^2}.$$
How would you determine where this function is non differentiable?
I've tried taking the partial derivative of $x$ and $y$, for general points, but i get stuck with an equation that i can't seem to simplify, is this the wrong method?
edit: ok so if for f(x) its differentiable at all points because its a rational function what about the max(x+2y,x^2+y^2), these are both rational, but the graph shows undefined points, how would you determine these points?
Recall that for the "Differentiability theorem" if all the partial derivatives exist and are continuous in a neighborhood of a point then (i.e. sufficient condition) the function is differentiable at that point.
In this case we can check that partial derivatives exist and are continuous in the domain, that is for $x^2+y^2\neq1$.