### The Maxima on-line user's manual

Algebra Calculator

#### Jacobian

Function: jacobian (<f>, <x>) Returns the Jacobian matrix of the list of functions <f> with respect to the list of variables <x>. The `(i, j)`-th element of the Jacobian matrix is `diff(<f>[i], <x>[j])`.

Examples:

```          (%i1) jacobian ([sin (u - v), sin (u * v)], [u, v]);
[ cos(v - u)  - cos(v - u) ]
(%o1)             [                          ]
[ v cos(u v)   u cos(u v)  ]
(%i2) depends ([F, G], [y, z]);
(%o2)                  [F(y, z), G(y, z)]
(%i3) jacobian ([F, G], [y, z]);
[ dF  dF ]
[ --  -- ]
[ dy  dz ]
(%o3)                      [        ]
[ dG  dG ]
[ --  -- ]
[ dy  dz ]```

```(%o1)                                true
(%i2) ```

### Related Examples

##### jacobian

jacobian ([x2 + dt*(x...

Calculate

##### jacobian

jacobian([f(x,y),g(x,...

Calculate

##### jacobian

f(x,y,z):=(x^2*(y+z),...

jacobian(f(x,y,z),[x,...

Calculate

##### jacobian

jacobian ([p+f_x*x/z,...

Calculate

##### jacobian

jacobian ([u^2*e^v, w...

Calculate

##### jacobian-solve

F:(0.05*x)*(1-(x/1500...

G:(0.25*y)*(1-(y/500)...

solve([F=0,G=0],[x,y]);

Calculate

##### jacobian

f(x,y):=[ 3*x+y, y-3*x];

jacobian(f(x,y),[x,y]);

Calculate

##### jacobian-tan

jacobian ([(x^2+y^2)^...

Calculate

##### jacobian

jacobian (x1*x2*x3-50...

Calculate

##### jacobian-matrix

m: matrix([p], [q], [...

jacobian(m,[u,v,p,q]);

Calculate