Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariate Bell Polynomials and Derivatives of Composed Functions   How do we take repeated derivatives of composed multivariate functions? for
one-dimensional functions, the common tools consist of the Fa\'a di Bruno
formula with Bell polynomials; while there are extensions of the Fa\'a di Bruno
formula, there are no corresponding Bell polynomials. In this paper, we
generalize the single-variable Bell polynomials to take vector-valued arguments
indexed by multi-indices which we use to rewrite the Fa\'a di Bruno formula to
find derivatives of $\textbf{f}(\textbf{g}(\textbf{x}))$.

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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin