WeBWorK Standalone Renderer

Suppose a change of coordinates $T : \mathbb{R}^2 \to \mathbb{R}^2$ from the $uv$ -plane to the $xy$ -plane is given by

$x = e^{-2u}\cos\!\left(3v\right), \ \ \ y = e^{-2u}\sin\!\left(3v\right).$
Find the absolute value of the determinant of the Jacobian for this change of coordinates.

$\displaystyle \left| \frac{\partial(x,y)}{\partial(u,v)} \right| = \bigg| \mathrm{det}$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$			$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

$\bigg| =$

You can earn partial credit on this problem.