# What is the derivative of e x

## Derive function

In this article, we'll explain how to use the **Derive function** can. We use the **Chain rule** and other **Derivation rules** and show you several examples.

You have entered derivation e function, derive e ^ x, derive e ^ -x, derive e to the power of x or something similar in the search engine you trust and landed here? Then you are exactly right!

You want to understand how to use the **Derive an exponential function** can? No problem! Just take a look at our video.

### E Derive function explained simply

The **Derivation **the** e function** is the function itself.

That means it applies:

You can easily remember that.

### Derive chain rule function

It only gets more difficult when you **e Derive functions** want expressions more complicated than just in their exponent have to stand.

### example 1

An example of this would be the function

In such a case you have to **Chain rule** apply to the **Derive function** to be able to. That's what you choose **inner function ** and** external function**, calculate their derivatives and and then puts it in the formula of the chain rule

a. In this example you will receive as

**inner function h and derivative h ‘:**

**outer function g and derivative g ‘:**

To determine the inner derivative you had to use the **Power-****and****Factor rule** apply.

If you put these results in the formula for the chain rule, you will eventually get it

### Example 2

Let's look at another example of the function derive:

In this case it is

**inner function h and derivative h ‘:**

**outer function g and derivative g ‘:**

If you plug the functions into the formula of the chain rule, you finally get

**Danger:** Be careful with assignments in which you **derive e** should. Because the solution would be zero there is in itself just a constant. Only when it is said, find the derivative of e to the power of x, is the correct answer for the derivative e ^ x.

### E function derive tasks

In addition to the chain rule, it can also be that you need to determine the derivative of an e function further **Derivation rules** need. In the following we present a few such examples or types of tasks in which you have to derive the e function:

### Further functions and their derivatives

You should also know the derivatives of the following functions by heart and be able to apply them:

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