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).

>>6

Are you sure I've got the right idea?

The function needs to have a real value at 0, but not be continous, that means functions of the form sin(1/x) won't work, because whilst they're not continous at (0,0) they don't have a defined value.

Is using the dirac delta function cheating? :p
Is that even continous, I doubt it.

It'd be x^2sin(1/x) + y^2sin(1/y) in my last example anyway, thinking about it. Not that it matters :p