# Implicit Function: What is It and Why Is It Used?

• MHB
• highmath
In summary, an implicit function is a mathematical relation expressed in the form of an equation that does not explicitly define any variable. It is used to describe relationships between variables that cannot be explicitly defined, particularly in complex systems. It differs from an explicit function in that it does not explicitly define any variable and is more complex. Some real-world applications of implicit functions include physics, engineering, economics, and computer science. In calculus, they are used in techniques such as implicit differentiation and integration.
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Why implicit function is a function?

https://mathhelpboards.com/calculus-10/implicit-function-24656.html are some answers to the same question.
My personal (Pavlovian) reaction would probably mention the implicit function theorem, but I think the discussion is best continued in that other topic.

## 1. What is an implicit function?

An implicit function is a mathematical relation between two or more variables that is expressed in the form of an equation. Unlike explicit functions, which explicitly define one variable in terms of another, implicit functions do not explicitly define any variable. Instead, the relationship between the variables is implied by the equation.

## 2. Why is implicit function used?

Implicit functions are used to describe relationships between variables that cannot be explicitly defined. They are particularly useful in situations where it is difficult or impossible to explicitly solve for one variable in terms of another. They are also commonly used in physics and engineering to describe complex systems and relationships.

## 3. How is an implicit function different from an explicit function?

The main difference between implicit and explicit functions is that implicit functions do not explicitly define any variable, while explicit functions explicitly define one variable in terms of another. Implicit functions are also typically more complex and cannot be easily graphed like explicit functions.

## 4. What are some real-world applications of implicit functions?

Implicit functions have many real-world applications, including in physics, engineering, economics, and computer science. They are used to describe relationships between variables in complex systems, such as in fluid dynamics, thermodynamics, and electrical circuits. They are also used in optimization problems and machine learning algorithms.

## 5. How are implicit functions used in calculus?

In calculus, implicit functions are used in implicit differentiation, which is a technique for finding derivatives of implicit functions. This is particularly useful when it is difficult or impossible to explicitly solve for one variable in terms of another. Implicit functions are also used in implicit integration, which is a technique for finding integrals of implicit functions.

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