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Download file# The Chain Rule for Higher Derivatives

journal contribution

posted on 01.11.1995, 00:00 by Walter NollPerhaps the most important theorem of elementary differential calculus is the Chain Rule. It states, roughly, that the composite of two differentiable functions is again differentiable, and it gives a formula for the derivative of this composite. A Chain Rule of Order n should state, roughly, that the composite of two functions that are n times differentiable is again n times differentiable, and it should give a formula for the n’th derivative of this composite. Many textbooks contain a Chain Rule of order 2 and perhaps 3, but I do not know of a single one that contains a Chain Rule of arbitrary order n with an explicit and useful formula. The main purpose of this paper is to derive such a formula.