Explicit Function
An explicit function is an algebraic function where the dependent variable can be explicitly expressed in terms of the independent variable. In simple words, we can say that explicit function is a function that is expressed more clearly and can be easily understood. In an explicit function, the input variable and out variable are separated by an equality sign '=' and hence, are on two different sides of the equal to sign. We can easily determine the dependent variable's value easily using the explicit function by simply inserting the value of the input in the function.
This article will explore the concept of explicit function, its definition, the difference between implicit and explicit function, and the derivative of an explicit function. We will also solve some examples for a better understanding of the topic.
| 1. | What is an Explicit Function? |
| 2. | Explicit Function Meaning |
| 3. | Difference Between Implicit and Explicit Function |
| 4. | Derivative of Explicit Function |
| 5. | FAQs on Explicit Function |
What is an Explicit Function?
An explicit function is a function in algebra in which the output variable (dependent variable) can be explicitly written only in terms of the input variable (independent variable). An explicit function usually involves two variables - dependent and independent variables. It is expressed more clearly and hence, it is easy to determine the values of the variables in an explicit function. On the other hand, a function that cannot be written as one variable in terms of the other variable is called an implicit function.
Explicit Function Meaning
In mathematics, an explicit function is defined as a function in which the dependent variable can be explicitly written in terms of the independent variable. In standard form, we can write an explicit function as y = f(x), where y is the output variable expressed completely in terms of the input variable x. In an explicit function, it is easy to find the value of the function corresponding to each value as the dependent variable is expressed clearly in terms of the input.
Difference Between Implicit and Explicit Function
Now, we know that implicit and explicit functions are generally treated as opposites of each other as the output variable is not expressed clearly in terms of the input variable in an implicit function. Sometimes an implicit function can also be converted into an explicit function by simplifying it. Given below are the main points highlighting the difference between implicit and explicit functions.
Implicit Function Vs Explicit Function
| Implicit Function | Explicit Function |
|---|---|
| An implicit function is a function with several variables, and one of the variables is a function of the other set of variables. | An explicit function is defined as a function in which the dependent variable can be explicitly written in terms of the independent variable. |
| General form of Implicit Function: f(x, y) = 0 | General Form of Explicit Function: y = f(x) |
| Example: xy + 2x - tan (xy) + y2 = 0 | Example: y = x + 2 |
Derivative of Explicit Function
The derivative of an explicit function is done regularly just like simple differentiation of algebraic functions. An explicit function is written as y = f(x), where x is an input and y is an output. The differentiation of y = f(x) with respect to the input variable is written as y' = f'(x). So, simple rules of differentiation are applied to determine the derivative of an explicit function. Let us solve a few examples to understand finding the derivatives.
Example 1: Find the derivative of the explicit function y = x2 + sin x - x + 4.
Solution: To find the derivative of y = x2 + sin x - x + 4, we will differentiate both sides w.r.t. x.
dy/dx = 2x + cos x - 1
Hence, the differentiation of y = x2 + sin x - x + 4 is dy/dx = 2x + cos x - 1.
Example 2: Find the derivative of the function xy - y = 0
Solution: First, we will express the given function explicitly.
xy - y = 0
⇒ y (x - 1) = 0
⇒ y = 1/(x - 1)
Now, we have expressed the given function as an explicit function. Next, we differentiate both sides of the function w.r.t. x.
dy/dx = -1(x - 1)2
Hence, the derivative of the given function is dy/dx = -1(x - 1)2
Important Notes on Explicit Function:
- An explicit function is a function in algebra in which the output variable (dependent variable) can be explicitly written only in terms of the input variable (independent variable).
- Some implicit functions can be converted into explicit functions.
- An explicit function is generally written as y = f(x).
- Explicit functions are used to find the coordinates of a graph.
☛ Related Topics:
FAQs on Explicit Function
What is an Explicit Function in Math?
In mathematics, an explicit function is defined as a function in which the dependent variable can be explicitly written in terms of the independent variable. In standard form, we can write an explicit function as y = f(x)
How to Identify Explicit Function?
A function in which the output variable can be clearly expressed in terms of the input variable, then we can say that the function is explicit.
How to Write Explicit Function in General Form?
In general form, we can write an explicit function as y = f(x), where y is the output variable expressed completely in terms of the input variable x.
What is the Difference Between Implicit and Explicit Functions?
An explicit function is an algebraic function where the dependent variable can be explicitly expressed in terms of the independent variable. On the other hand, a function that cannot be written as one variable in terms of the other variable is called an implicit function.
Give Some Examples of Explicit Function.
Some of the examples of explicit function are:
- y = x + cos x
- y = x2 - x + 3
- y = xy - 5
How to Check if a Function is an Explicit Function?
To check if a function is an explicit function, we simplify it and try to express the dependent variable in terms of the independent variable. If we can express in such a way, then we can say that the function is explicit, else it is not.