Abstract: Disclosed are methods for structurally differentiating polynomial functions using parallelogrammic elements. The methods include representing a first ordered pair defined by the polynomial function as a construction of such structural elements. Second or sequent sets are also similarly constructed for an ordered pair defined by a different variable value. The resulting structural sets are compared to determine differences and the differential is expressed either directly or after dividing by the associated change in the variable of the polynomial function used to construct the two or more sets of elements.

Abstract: Methods for structurally differentiating functional relationships between two ordered sets of numbers related as x and one or more functions of x. The methods employ constructing sets of structural elements into parallelograms and any remainder portions. The parallelograms are constructed with at least one side of each having the same lengths or number of units. The structural elements of the sets are also arranged so that any remainder portions of both sets are also equal. The difference in total number of parallelogrammic units is then computed and divided by the difference in the variable x to produce the derivative value sought.