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Computing partial derivatives


*****

Problem:

Compute the partial derivatives with respect to x and y for

> f := (x,y) -> sin(sqrt(x))*log(y^2);

                                                       2
                      f := (x, y) -> sin(sqrt(x)) log(y )

and evaluate them at (1,1/2).



Answer:


Just do it!


w.r.t. x is fx given by

> fx := diff(f(x,y),x);

                                         1/2      2
                                    cos(x   ) ln(y )
                          fx := 1/2 ----------------
                                           1/2
                                          x

and w.r.t. y is fy given by

> fy := diff(f(x,y),y);

                                            1/2
                                       sin(x   )
                               fy := 2 ---------
                                           y

For the purposes of evaluation it is more convenient to use the "D" operator. Hence, the value of the partial w.r.t. x evaluated at (1,1/2) is given by,

> D[1](f)(1.,0.5);

                                 -.3745090200

and fy(1,1/2) is given by,

> Dfy := unapply(fy,(x,y));

                                                 1/2
                                            sin(x   )
                         Dfy := (x, y) -> 2 ---------
                                                y

Now apply,

> Dfy(1.,0.5);

                                  3.365883940

Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>
Last modified: Thu Mar 29 15:26:10 EST 2001