The Jacobian([f(x,y,...), g(x,y,...), ...], [x,y,...]) calling sequence returns the matrix form of the Jacobian. The calling sequence in the form Jacobian([f(x,y,...), g(x,y,...),...], [x,y,...]=[a,b,..]) returns the matrix form of the Jacobian evaluated at a point specified by $\[a,b,...\]$. The dimension of the point must equal the number of independent variables.

Specifying the option output = method returns the Jacobian in the specified form, where method is one of determinant or matrix. The matrix form is the default.

If the output = determinant option is given, then the number of independent variables must equal the number of algebraic expressions.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\right)\:$

$\mathrm{Jacobian}\left(\left[x+y^2\right]\,\left[x\,y\right]\right)$

$\left[\begin{array}{cc}1& 2y\end{array}\right]$

$\mathrm{Jacobian}\left(\left[x+y^2\right]\,\left[x\,y\right]=\left[1\,-1\right]\right)$

$\left[\begin{array}{cc}1& \mathrm{-2}\end{array}\right]$

$\mathrm{Jacobian}\left(\left[zx+y-4\,z+x-y\,z^2\right]\,\left[x\,y\,z\right]=\left[1\,2\,C\right]\right)$

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

$\mathrm{Jacobian}\left(\left[zx+y-4\,z+x-y\,z^2\right]\,\left[x\,y\,z\right]=\left[1\,2\,C\right]\,\mathrm{output}=\mathrm{determinant}\right)$

$-2C^2-2C$

$\mathrm{Jacobian}\left(⟨x\,x-y⟩\,\left[x\,y\right]\,\mathrm{output}=\mathrm{matrix}\right)$

$\left[\begin{array}{cc}1& 0\\ 1& \mathrm{-1}\end{array}\right]$