What is a function which differs when differentiated with respect to $x$ and then with $y$ to function differentiated with respect to $y$ and then $x$? Even if it differs at one particular point.
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3http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives#Requirement_of_continuity – Zev Chonoles Apr 22 '15 at 04:05
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More advanced: Can cross partial derivatives exist everywhere but be equal nowhere? – Apr 22 '15 at 04:31