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).

>>3, 4
What do you mean by double cone?  I phail to see a 2nd cone.

>>6
By that requirement, >>2 would also fail due to the 0/0 singularity in the partial derivatives at (0,0).