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**ANSWER**

This is the reason that the exponential function with the base e is special. e is the unique number a, such that the value of the derivative of the exponential function f (x) = a x (blue curve) at the point x = 0 is exactly 1.

The** function** y=ex is often referred to as simply the** exponential function.** Besides the trivial case f (x)=0, the** exponential function** y=ex is the only function whose derivative is equal to itself. Similarly, it is asked, why e x is its own derivative? DERIVATIVE OF THE EXPONENTIAL FUNCTION.

What's so special about the Euler number e? It is the answer to the question: What **function** will become its own derivative? Say that you didn't know what [math]e[/math] was, but you wanted to find out. You only had the question above in mind so that[math] f(x)=e^x[/math], and you knew that

What Is an Exponential Function? In an **exponential function**, the independent variable, or x-value, is the exponent, while the base is a constant. For example, y = 2 x would be an **exponential function**. Here's what that looks like.

How are exponential and logarithmic functions related ? **Exponential** Expression. In mathematics, an **exponential function** is defined as a type of expression where it consists of constants, variables, and exponents.

The purpose of exponential function is to represent total output to an input that grows at every moment at a rate specified in exponent of the exponential function. Its shown that if 1 grows every moment double and if you microscopically divide and see its growth for 1 …

What Is Exponential Growth? **Exponential** growth is a pattern of data that shows greater increases with passing time, creating the curve of an **exponential function**.

What is an Exponential Function? As you can see from the figure above, the graph of an **exponential function** can either show a growth or a decay. The figure on the left shows **exponential** growth while the figure on the right shows **exponential** decay. Examples of **exponential functions** 1. y = 0.5 × 2 x 2. y = -3 × 0.4 x 3. y = e x 4. y = 10 x Can you tell what b equals to for the

Definition of **exponential function** in the **Definitions.net** dictionary. Meaning of **exponential function**. What does **exponential function** mean? Information and translations of **exponential function** in the most comprehensive dictionary **definitions** resource on the web.

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