2006/02/09 by Levy, Eliahu
#FOS: Mathematics #Functional Analysis (math.FA) #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.math/0602183
It is well-known that the coefficients in Faa di Bruno's chain rule for higher derivatives can be expressed via numeration of partitions. It turns out that this has a natural form as a formula for the vector case. To this formula two proofs are presented, both "explaining" its form involving partitions: one as a purely algebraic fact, and one "from first principles" for the case of Frechet derivatives of mappings between Banach spaces.