Implicit Function Theorem

Creator
Creator
Seonglae ChoSeonglae Cho
Created
Created
2022 Nov 14 18:35
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Edited
Edited
2025 Oct 19 16:42
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IFT

Also called the fixed point theorem, it is a mathematical theorem that guarantees that even when the relationship between functions is not direct, it can be expressed as a single function in the neighborhood.
In cases where and are implicitly related by an equation and y cannot be explicitly expressed as a function of x, the Implicit Function Theorem (IFT) states that if the partial derivative is invertible, then locally there exists a differentiable function satisfying . In this neighborhood, the derivative of y with respect to x can be computed as:
 
 
 
 
 
 

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