The jacobian(F,v) function computes the Jacobian matrix of F with respect to the variable(s) v.

Each row of the result corresponds to the partial derivatives of an entry in F with respect to the entries of v.

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$\mathrm{M1}≔\mathrm{Matrix}\left(2\,3\,'\mathrm{fill}'=12x^2{y}^3\right)\:$

$\mathrm{M2}≔\left[x\,y\right]\:$

$\mathrm{jacobian}\left(\mathrm{M1}\,\mathrm{M2}\right)$

$\left[\begin{array}{cc}24x{y}^3& 36x^2{y}^2\\ 24x{y}^3& 36x^2{y}^2\\ 24x{y}^3& 36x^2{y}^2\\ 24x{y}^3& 36x^2{y}^2\\ 24x{y}^3& 36x^2{y}^2\\ 24x{y}^3& 36x^2{y}^2\end{array}\right]$