# 3.3  Differentiating Expressions
# Art Belmonte, Summer 1996
# These are the shaded gray examples which appear in Section 3.3.
> restart; diff(3*x^2 + 4*x^3, x);

                                       2
                             6 x + 12 x

> f:=3*x^2 + 4*x^3;

                                   2      3
                           f := 3 x  + 4 x

> Df:=diff(f, x);

                                          2
                          Df := 6 x + 12 x

> subs(x=2, Df);

                                  60

> f:=cos(t^2)^2;

                                      2 2
                            f := cos(t )

> diff(f, t);

                                 2       2
                         -4 cos(t ) sin(t ) t

> diff(f, t$2);

                 2 2  2          2 2  2          2       2
          8 sin(t )  t  - 8 cos(t )  t  - 4 cos(t ) sin(t )

>