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depends-hessian

hessian (4*x^2 + 4*y^...

depends (F, [a, b]);

hessian (F, [a, b]);

Calculate

depends-diff

depends(y,x);

eqn:((x^3+y^3)/(xy))=3;

de:diff(eqn, x);

Calculate

depends-hessian

hessian ( x^2-y^2+x*y...

depends (F, [a, b]);

hessian (F, [a, b]);

Calculate

depends-hessian

hessian (8*x^3 - 9*x^...

depends (F, [a, b]);

hessian (F, [a, b]);

Calculate

depends-jacobian

jacobian ([u+v, u], [...

depends ([F, G], [y,...

jacobian ([F, G], [y...

Calculate

depends-jacobian

jacobian ([4*u/v, 8*v...

depends ([F, G], [y,...

jacobian ([F, G], [y...

Calculate

depends-jacobian

jacobian ([(u^2)-1, (...

depends ([F, G], [y,...

jacobian ([F, G], [y...

Calculate

depends-exp-hessian

hessian ((0.5*(((2*(x...

depends (F, [a, b, c]);

hessian (F, [a, b, c]);

Calculate

depends-hessian

hessian (x^2 +(2*y^2)...

depends (F, [a, b]);

hessian (F, [a, b]);

Calculate

depends-hessian

hessian (x^3, y^3);

depends (F, [a, b]);

hessian (F, [a, b]);

Calculate

depends

Run Example
(%i1)gradef(r(t),drdt);
(%o1)                                r(t)
(%i2) depends(r, t);
(%o2)                               [r(t)]
(%i3) v:diff(r, t);
                                      dr
(%o3)                                 --
                                      dt
(%i4) e:(a-r^3)^(1/3);
                                        3 1/3
(%o4)                             (a - r )
(%i5) w:diff(e, t);
                                       2 dr
                                      r  --
                                         dt
(%o5)                            - -----------
                                         3 2/3
                                   (a - r )
(%i6) f:w^2;
                                    4  dr 2
                                   r  (--)
                                       dt
(%o6)                             -----------
                                        3 4/3
                                  (a - r )
(%i7) plot2d(diff(f,t), [r, -10, 10]);
plotplot2d(diff(f,t), [r, -10, 10]);
Run Example
hessian ((x+y+z)^2, [x, y, z]);
                                  [ 2  2  2 ]
                                  [         ]
(%o1)                             [ 2  2  2 ]
                                  [         ]
                                  [ 2  2  2 ]
(%i2)  depends (F, [a, b]);
(%o2)                              [F(a, b)]
(%i3)  hessian (F, [a, b]);
                               [   2      2   ]
                               [  d F    d F  ]
                               [  ---   ----- ]
                               [    2   da db ]
                               [  da          ]
(%o3)                          [              ]
                               [   2      2   ]
                               [  d F    d F  ]
                               [ -----   ---  ]
                               [ da db     2  ]
                               [         db   ]
(%i4) 
Run Example
hessian (-x^2-y^2-x*y, [x, y]);
                                 [ - 2  - 1 ]
(%o1)                            [          ]
                                 [ - 1  - 2 ]
(%i2)  depends (F, [a, b]);
(%o2)                              [F(a, b)]
(%i3)  hessian (F, [a, b]);
                               [   2      2   ]
                               [  d F    d F  ]
                               [  ---   ----- ]
                               [    2   da db ]
                               [  da          ]
(%o3)                          [              ]
                               [   2      2   ]
                               [  d F    d F  ]
                               [ -----   ---  ]
                               [ da db     2  ]
                               [         db   ]
(%i4) 
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