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

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