Discontinuous, But Partial Derivatives Exist

z = (1/4) [1 + (x^2 + y^2)^(3/2)] cos(4 arctan(y, x)), from Calvis, College Math. Journal, Jan 2000. It is discontinuous at the origin but has partial derivatives everywhere.

Created by Wolfram Mathematica 6.0  (28 October 2007)