implicit function theorem (Q6482807)

theorem that, under a mild condition on the partial derivatives, the set of zeros of a system of equations is locally the graph of a function

Language	Label	Description	Also known as
English	implicit function theorem	theorem that, under a mild condition on the partial derivatives, the set of zeros of a system of equations is locally the graph of a function

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instance of

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inverse function theorem

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studied in

calculus

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Implicit circle.svg
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the implicit function theorem guarantees that, on the level curve 𝑓(𝑥,𝑦)=1 of the function 𝑓(𝑥,𝑦)=𝑥²+𝑦², near the point 𝐀, 𝑦 can be expressed as a function of 𝑥; no such function, however, exists near the point 𝐁 (English)

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defining formula