The derivative operator D

The D operator has been extended to handle partial derivatives. The notation D[i](f) means the derivative of with respect to the 'th argument. The chain rule is applied and, by default, it is assumed that partial derivatives commute. Examples:

    > g := (x,y) -> sin(x+cos(y)):
    > D[1](g);
                            (x,y) -> cos(x + cos(y))

    > D[1,2](g);
                        (x,y) -> sin(x + cos(y)) sin(y)

Consequently, the mtaylor function (for multivariate Taylor series) will now expand an unknown function of more than one argument, e.g.

    > readlib(mtaylor): # load the mtaylor routine
    > mtaylor(f(x,y),[x=0,y=0],3);

                                                                       2
   f(0, 0) + D[1](f)(0, 0) x + D[2](f)(0, 0) y + 1/2 D[1, 1](f)(0, 0) x

                                                           2
            + D[1, 2](f)(0, 0) x y + 1/2 D[2, 2](f)(0, 0) y