How to determine if a piecewise function is differentiable?

Question

In particular, I've this function in R^2:

f = Piecewise[ { {(x y) / (x^2 +y^2), x != 0 && y != 0}, {0, x == 0 && y == 0} } ]

Now I would like to determine if the function is differentiable at point (1,2) without using the definition. I remember that in Wolfram alpha there's an simply "is differentiable?", but there I can't set an specific point.. So can I use same simple mathematica function? Ps I know use the definition of differentiability, but at the moment I need something faster if possible

Here's a similar question. – A little mouse on the pampas Jul 28 '20 at 01:43 — A little mouse on the pampas, Jul 28 '20 at 01:43

score 3 · Answer 1 · answered Jul 28 '20 at 01:38

I think you might find the answer given in this link useful, it gives an example of a piecewise function and how to find the non-differentiable points

How to find the non-differentiable point(s) of a given continuous function?

It is only a matter of generalizing for two variables, and checking if that specific point you are looking for is part of the non-differentiables or not

Hope that helps.

How to determine if a piecewise function is differentiable?

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