Differentiation and Integration

Differentiation is performed using the diff command:

> # Take the first-order derivative of an expression w.r.t. x:
> diff(3*x^2, x);
6 x
> # Take higher-order partial derivatives by specifying a sequence
> # of variables.  Derivatives are taken in the same order as the 
> # variable sequence:
> diff(y * x^2 + y, x, y);
2 x

Definite and indefinite integration are performed using the int command,
in the same way as described for the sum command:

> # An example of indefinite integration:
> int( cos(x), x );
sin(x)
> # An example of definite integration:
> int( x^2, x=0..2 );
8/3
> # An example where Maple can't find the solution:
> int(x^(-2), x=-1..1);
                              1
                              /
                             |    1
                             |  ---- dx
                             |    2
                            /    x
                            -1

When Maple is unable to find the solution to a problem, it returns a
"prettyprinted" version of the original command expression.  Sometimes
this will be because Maple doesn't know how to solve the problem, but
more often it will be because either no solution exists or the original
command/query was not posed properly.