##  [Implicit Function Theorem](/implicit-function-theorem) 

  ##  [Implicit Function Theorem](https://natural.quantumdictionary.io/implicit-function-theorem-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A local statement guaranteeing that, near a point where a system of differentiable equations F(x,y)=0 has a nondegenerate Jacobian with respect to y, there exists a differentiable map y = g(x) solving the system in a neighborhood of that point.

 

 

 

 

 





 

 



 ##  [Implicit Function Theorem](https://puremath.quantumdictionary.io/implicit-function-theorem-1) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A local result that guarantees, under differentiability and a nonsingular Jacobian condition with respect to certain variables, the ability to solve an equation F(x,y)=0 for y as a differentiable function y=g(x) near a base point.