A mixed second partial derivative

For $f(x,y)=x^2 y^2 + x^3 y$ , evaluate the mixed second partial $\dfrac{\partial^2 f}{\partial x\,\partial y}$ at the point $(x,y)=(1,2)$ .

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Differentiate first in $y$ (hold $x$ fixed), then in $x$ (hold $y$ fixed).
$\partial f/\partial y = 2x^2y + x^3$ ; now take $\partial/\partial x$ , then plug in $(1,2)$ .

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Asked at: Probability & Market-Making, Game-Based Aptitude