{"paper":{"title":"How to stare at the higher-order n-dimensional chain rule without losing your marbles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Henry O. Jacobs","submitted_at":"2014-10-13T20:06:24Z","abstract_excerpt":"Given two real functions on the real line f and g, the Faa di Bruno provides the higher order derivative of the composition of f and g, as a summation over the lower order derivatives of f and g individually. The corresponding multi-dimensional generalization is substantially more difficult due to the complicated combinatorial considerations one must take into account when dealing with standard multi-indices. In this note we provide a simple statement and derivation of the multi-dimensional Faa di Bruno formula by resorting to notions from multiset theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3493","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}