## Definition

A Functional Exponent is a function in the form of f(x) = a^{x}, where x is a variable and a is a constant, and it is known as the base of the function and should be greater than 0. Functional exponent is also called exponential function.

**Forms of Functional Exponent**

- f(x) = a
^{x} - f(x) = ba
^{x}, where b is also a constant - f(x) = e
^{x} - f(x) = pe
^{qx}, where p is also a constant

**Examples of Functional Exponent**

The most common example of the functional exponent is e^{x}, where the value of e is 2.718. Some other examples are as follows:-

- 5e
^{15x} - (1/2)
^{x} - 7(8)
^{-0.7x}, etc.

**Properties of Functional Exponent**

- a
^{0}= 1 - (a
^{m})^{n }= a^{m x n} - a
^{m}x a^{n}= a^{(m + n)} - a
^{m}/ a^{n}= a^{(m – n)} - (a x b)
^{m}= a^{m}x b^{m} - (a / b)
^{m }= a^{m}/ b^{m} - a
^{-m}= 1/a

**Relation between ****Functional Exponent** and Logarithmic Functions

**and Logarithmic Functions**

**Functional Exponent**If there is any functional exponent that is in the form of:-

p^{x} = b

Then, it can be written as:-

log _{p} b = x

So, the relation between Functional Exponent and Logarithmic Functions is:-

p^{x} = b => log _{p} b = x

## Some **Graphs of ****Functional Exponent**

**Functional Exponent**### 1. Graph of 5^{x}

Let, f(x) = 5^{x} . So, some values of f(x) will be-

So, the Graph of 5^{x } will be:-

### 2. Graph for (1/2)^{x}

Let f(x) = (1/2)^{x}. So, some values of f(x) will be-

So, the Graph of (1/2)^{x} will be:-

### 3. Graph of e^{x}

Let f(x) = e^{x}. So, some values of f(x) will be-

Value of e = 2.718

So, the graphs of the e^{x} will be-

## Derivative of **Functional Exponent** or Exponential Function

**Functional Exponent**- d/dx (e
^{x}) = e^{x} - d/dx (a
^{x}) = a^{x}log a

## Integration of **Functional Exponent**s

**Functional Exponent**- ∫ e
^{x}dx = e^{x}+ C - ∫ a
^{x}dx = (a^{x}/ log a) + C

Where C is a constant.

## Series Expansion of e^{x}

So, What is a functional exponent? The answer is functional exponent is the same as the exponential functions that we see in Mathematics, it’s just that we are calling exponential functions a functional exponent. We have seen most of the required things anyone needs to know about functional exponents. We hope this article on the Exponetinial Function Helps you.

If you have any questions/doubts in mind, please use the comments below.

Thank you for reading this article, click here to start learning Python in 2022.

**Also Read:**

- I Love You Text in ASCII Art
- Python Turtle Shapes- Square, Rectangle, Circle
- Python Turtle Commands and All Methods
- Happy Birthday Python Program In Turtle
- I Love You Program In Python Turtle
- Draw Python Logo in Python Turtle
- Space Invaders game using Python
- Draw Google Drive Logo Using Python
- Draw Instagram Reel Logo Using Python
- Draw The Spotify Logo in Python Turtle
- Draw The CRED Logo Using Python Turtle
- Draw Javascript Logo using Python Turtle
- Draw Dell Logo using Python Turtle
- Draw Spider web using Python Turtle
- Draw Chrome Logo using Python Turtle
- Draw Virus using Python Turtle
- Draw Apple Logo Using Python turtle
- Creating a Facebook Logo Using Python Turtle
- Draw a boat using Python Turtle
- Draw the Shaktiman Logo using Python Turtle
- Draw WhatsApp Logo Using Python Turtle
- Draw PUBG Logo Using Python Turtle
- Draw Snowflakes using Python Turtle
- Draw a house using Python Turtle
- Draw a Galactic Flower Using Python Turtle
- Draw a Spiderman logo using Python Turtle
- Draw Spiral Shapes using Python Turtle
- Creating a Pong Game using Python Turtle
- Draw an Android Logo using Python Turtle
- Draw Snowman using Python Turtle