Let $f(x, y, z) = 6xy - z^2$, $x = 4r \cos(\theta)$, $y = \cos^2(\theta)$, $z = 6r$.
Use the Chain Rule to calculate the partial derivative.
(Use symbolic notation and fractions where needed. Express the answer in terms of independent variables.)
$\frac{\partial f}{\partial \theta} = -72r^2 \cos^2(\theta) \sin(\theta)$