Monsieur Ejemplé

Give an example of a function f:R^2 --> R where both partial derivatives df/dx and df/dy exist non-trivially, but neither are continuous at (0,0).

>>13

Is the power of 3/2 really needed?
This makes it not continous at 0 by not having a bounded value, but with a power of 2 you get the same result, but instead of it being unbounded it just does not approach a limit.

Also I can get rid of the x and y terms in my answer, then the derivative at (0,0) would be 0, but the function would oscillate wildy between 1 and -1 as it approached 0.

Meh, I just think x^2sin(1/x) + y^2sin(1/y) is somehow a bit more....aesthetically pleasing than x^(3/2)sin(1/x) + y^(3/2)sin(1/y). No idea why.

I think the boundedness pleases me :p