Seonglae ChoIFT
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:
Implicit function theorem - Wikipedia
In mathematics, more specifically in multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does so by representing the relation as the graph of a function.
https://en.wikipedia.org/wiki/Implicit_function_theorem