Measuring the Twist

Consider the surface

$f(x, y) = x^3 \ln y + e^{\,2xy}$

defined for $y > 0$.

Compute the mixed second-order partial derivative $f_{xy}$ — that is, differentiate with respect to $x$ first, then differentiate the result with respect to $y$ — and evaluate it at the point $(1,\ 1)$.

What do you get?