Evaluating formulae of network functions and their derivatives are introduced in this paper. The algorithm of network analysis and optimization will be more efficient by using these formulae.

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.

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.