Symmetry of second derivatives

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In mathematical analysis, the symmetry of second derivatives (also called the equality of mixed partials) is the fact that exchanging the order of partial derivatives of a multivariate function f ( x 1 , x 2 , … , x n ) {\displaystyle f\left(x_{1},\,x_{2},\,\ldots ,\,x_{n}\right)} does not change the result if some continuity conditions are satisfied (see below); that is, the second-order partial derivatives satisfy the identities ∂ ∂ x...

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