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This report describes automatic differentiation, which is neither symbolic nor approximate, for single functions of one real variable. The rules of evaluation and differentiation are combined into an ordered-pair arithmetic similar to complex arithmetic, but slightly simpler. Evaluation of the formula for a function in this arithmetic yields both the values of the function and its derivative, without a formula for the derivative of the function, and without numerical approximation, since this arithmetic is baed on the well-known rules for differentiation. The properties of this arithmetic are examined, and illustrated by simple examples. Subroutines are given for differentiation arithmetic both on a hand-held programmable calculator, and in the microcomputer language Pascal-SC. An application of this arithmetic to the solution of equations by Newton's method is given, using a Pascal-SC program. (Author)
L. B. Rall (Mon,) studied this question.