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If the partial derivatives of f are differentiable, we get the second order derivatives of f, and so on.
) be a function of two variables having partial derivatives fx
on an open domain
and if the partial derivatives are all continuous
As a first example, see Ex. 5.13.
The computation of the mixed second derivative, in reversed order, is much more complicated:
We can iterate the above description and define the partial derives of order higher than 2, namely
and so on.