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arXiv · 2212.10172

On Higher Partial Derivatives of Implicit Functions and their Combinatorics

Shaul Zemel
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Abstract

We consider a scalar-valued implicit function of many variables, and provide two closed formulae for all of its partial derivatives. One formula is based on products of partial derivatives of the defining function, the other one involves less products of building blocks of multinomial type, and we study the combinatorics of the coefficients showing up in both formulae.

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Shaul Zemel. 2022-12-20. On Higher Partial Derivatives of Implicit Functions and their Combinatorics. https://arxiv.org/abs/2212.10172

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