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-andFactor 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: