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This document discusses using SymPy, a Python symbolic mathematics library, to verify that the partial derivatives of the function f(x,y) = x*y^2*ln(x^2) are the same regardless of derivative order. It provides code to calculate all combinations of partial derivatives with respect to x and y using nested for loops over the variables, and check if they are equal to 2x + y. It also notes that log(x) is equivalent to ln(x) in SymPy.Read less