Grad

Grad(function, list-of-variables)

gives the gradient of the function.

Grad({f1, f2,...},  {v1, v2,...})

returns the Jacobian matrix for the vector of functions.

See:

>> Grad(2*x+3*y^2-Sin(z), {x, y, z})
{2,6*y,-Cos(z)}

Create a Jacobian matrix:

>> Grad({f(x, y),g(x,y)}, {x, y})
{{Derivative(1,0)[f][x,y],Derivative(0,1)[f][x,y]},{Derivative(1,0)[g][x,y],Derivative(0,1)[g][x,y]}}

Example from Wikipedia where the Jacobian matrix doesn’t need to be squared:

>> Grad({x1,5*x3,4*x2^2-2*x3,x3*Sin[x1]},{x1,x2,x3})
{{1,0,0},{0,0,5},{0,8*x2,-2},{x3*Cos(x1),0,Sin(x1)}}