Deriving Fa\`a di Bruno's formula for the derivative of a composite function via compositions of integers
Abstract
We give yet another proof for Fa\`a di Bruno's formula for higher derivatives of composite functions. Our proof technique relies on reinterpreting the composition of two power series as the generating function for weighted integer compositions, for which a Fa\`a di Bruno-like formula is quite naturally established.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.