Chain Rules for Higher Derivatives

Huang, H.-N.; Marcantognini, S. A. M.; Young, N. J.
March 2006
Mathematical Intelligencer;Spring2006, Vol. 28 Issue 2, p61
Academic Journal
The article presents a definition of the concept of higher-order directional derivative of a smooth function. It is then applied to create three simple formulas for the nth derivative of the composition of two functions. These three higher-order chain rules are alternatives to the classical formula of Faa di Bruno. They are less explicit but are much simpler and are not saddled with Diophantine or combinatorial problems.


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