$f(x,y)=\frac{x^3y-xy^3}{x^2+y^2}$, defined as 0 at 0 looking at its mixed partial derivatives $\partial_{xy}f,\partial_{yx}f$ specifically and how they don't match.
Why does this function not contradict Clairaut's theorem?
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real-analysis
multivariable-calculus
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2Well, there is only *one* hypothesis in Clairaut's Theorem and that's the continuity of partial derivatives at that point. So if not contradicting good chance this hypothesis isn't met... – 2017-01-13
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0$f$ is not of class $C^2$ – 2017-01-13