Show directly (i.e., without Clairaut’s theorem) that if f(x, y)=xnym, where m and n are nonnegative integers, then ∂2 f/∂y∂x = ∂2 f/∂x∂y. Use this to show that if f(x, y) is any polynomial, then ∂2 f/∂y∂x = ∂2 f/∂x∂y.
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