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Mixed Partial Derivatives

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Assume that $ f = f(x_1, \ldots, x_n)$ has continuous second partial derivatives. Then

$\displaystyle \partial_i\partial_j f = \partial_j\partial_i f\, . $

Thus, if $ f$ is sufficiently smooth, mixed partial derivatives are independent of the ordering of the variables.

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  automatically generated 5/30/2011