I have this funtion: and if
so if I want to demonstrate it is differentiable in , here is what I do:
1) I check if is continuous in .
2) I find partial derivatives.
3) I check if partial derivatives are continuous in (0,0).
In case steps 1) and 3) are affirmatives, the function is differentiable in .
So, in this case:
1)It is continuous.
2) I calculate partial derivate respect x:
When I calculate the limit of partial derivate respect in (0,0) and it doesn't exit, so partial derivates are not continuos in so is not differentiable,
Thank you very much! Great forum!