$x^2\+y z\,2-x y\,y^2-z$

$x^2\+yz\,2-xy\,y^2-z$

$x\,y\,z$

$x\,y\,z$

$\left[1\,2\,a\right]$

$\left[1\,2\,a\right]$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{Jacobian}\right]\left(\left[\right]\,\left[\right]\right)$

$\left[\begin{array}{ccc}2x& z& y\\ -y& -x& 0\\ 0& 2y& -1\end{array}\right]$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{Jacobian}\right]\left(\left[\right]\,\left[\right]\=\right)$

$\left[\begin{array}{ccc}2& a& 2\\ -2& -1& 0\\ 0& 4& -1\end{array}\right]$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{Jacobian}\right]\left(\left[\right]\,\left[\right]\,\mathrm{output}\=\mathrm{determinant}\right)$

$2x^2-2y^3-yz$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{Jacobian}\right]\left(\left[\right]\,\left[\right]\=\,\mathrm{output}\=\mathrm{determinant}\right)$

$-14-2a$