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For a function of more than one variable, say f(x,y), a mixed partial derivative is a derivative formed by partial differentiation with respect to more than one of the variables, one after another, for instance [( ∂² f)/( ∂x ∂y )] means f differentiated with respect to x, and then y.
For analytic functions (ie most 'ordinary' functions) the order of the differentiations does not matter, but for some unusual functions this is not the case.