2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108902It 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.10 pagesGeneral MathematicsFunctional Analysistext