# 3.2  Differentiating Functions
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 3.2.
> restart; f:=x->x^2 * (x^5 + 1);

                                   2   5
                        f := x -> x  (x  + 1)

> D(f);

                                  5           6
                       x -> 2 x (x  + 1) + 5 x

> D(f)(2);

                                 452

> f:=x->(x^3 - 1) / (x + 2);

                                      3
                                     x  - 1
                           f := x -> ------
                                     x + 2

> m:=D(f)(2);

                                    41
                               m := --
                                    16

> y:=m*(x - 2) + f(2);

                                41
                           y := -- x - 27/8
                                16

>