Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Why do partitions occur in Faa di Bruno's chain rule for higher
  derivatives?   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.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: math-ph