For any (x,y) other than (0,0).
For (x,y) = (0,0)
f(x,y) = 0
Is f totally differentiable?
The Attempt at a Solution
If the function is not continuous, it can't be differentiable.
So the limit doesn't exist.
However I looked at the solution and it is differentiable. Is it possible that the solution is wrong or did I make a mistake?
Thanks for your help.
Edit: I don't why it doesn't TeX (at least on my browser) so:
f(x,y) = tan(xy)*sin(1/[x^2+y^2])
And for my attempt at a solution:
lim(x,y->0,0) f(x,y) = lim (x,y->0,0) xy/(x^2+y^2) = lim (r -> 0) cos T*sin T