= Symmetry of second derivatives
{title2=$\partial_i\partial_jf=\partial_j\partial_if$}
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= Clairaut's theorem
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When the second <partial derivatives> are continuous in a neighborhood, the order of the <mixed partial derivatives> can be interchanged. Expressing a rectangular finite difference as either iterated integral by the <fundamental theorem of calculus> and shrinking the rectangle proves the equality. Mere existence of both derivatives does not imply this symmetry.
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