Abstract: Evaluation relevant to the partial derivatives of the multivariable functions is often done in scientific computation, usually by means of the symbolic differentiation or the divided difference. But for the middle and large scale problems, the computation cost by symbolic differentiation is very expensive. When the direction derivative is evaluated, the computation cost by divided difference can be reduced, but it is only one kind of aproximate computation. Moreover, it is very difficult to confirm the divided difference interval rightly. Automatic differentiation, by which the derivatives of the function can be evaluated both exactly and economically, is applied to the field of scientific and engineering computation extensively.