Generalization of the formula of Faa di Bruno for a composite function with a vector argument

By R. Mishkov. 2000

93 citations recorded by the source corpus.

The paper presents a new explicit formula for the nth total derivative of a composite function with a vector argument. The well-known formula of Faa di Bruno gives an expression for the nth derivative of a composite function with a scalar argument. The formula proposed represents a straightforward generalization of Faa di Bruno's formula and gives an explicit expression for the nth total derivative of a composite function when the argument is a vector with an arbitrary number of components. In this sense, the for- mula of Faa di Bruno is its special case. The mathematical tools used include differential operators, polynomials, and Diophantine equations. An example is shown for illustration.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/90b071a21c0ff8f611e4ab25315f369bf1da4805

How researchers see this paper

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In Algebra and Number Theory

1. N. Young
2. Huang-Nan Huang
3. S. Marcantognini

In Applied Mathematics

1. N. Young
2. Huang-Nan Huang
3. S. Marcantognini
4. Jim Agler

Citations in the corpus

• Chain rules for higher derivatives (2006, result): “It wou ld be surprising if anything new could be said about such a classical topic, but we have not found anything similar in [8] or other recent papers [2, 9, 11].”