# A Finite Algorithm for the Exact Evaluation of Higher-Order Partial Derivatives of Functions of Many Variables

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## Abstract

This article develops an algorithm for the exact forward-mode automatic evaluation of higher order partial derivatives using derivative arrays, now referred to as the FEED (Fast Efficient Evaluation of Derivatives) algorithm. Building on previous work by R. Wengert, the FEED algorithm proceeds by decomposing the evaluation of complicated functions of many variables into a sequence of simpler evaluations of special functions of one or two variables. Annotated pointers to related work can be accessed here: http://www.econ.iastate.edu/tesfatsi/nasahome.htm

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