Abstract: The present invention provides a novel method and apparatus for the automatic evaluation of partial derivatives. A computer memory system is organized and controlled so that partial derivatives are evaluated, without approximation, for any given function at specified values of the independent variables of the function. The method involves parsing the given function and assigning codes, including priority order, to each function element. The function elements are then examined individually along with their priority codes by an interpreter which determines when an operation should be performed. To perform operations which result in the evaluation of partial derivatives, there is provided an evaluation matrix to organize and store values, and an evaluator which is used to manipulate the evaluation matrix for operations specified by the interpreter. The evaluator performs manipulations on the evaluation matrix by using a number of sets of instructions which are derived from the rules defining partial derivatives.