# Solving the Derivative of cos(2x) Video

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Solving the Derivative of cos(x)

### You're on a roll. Keep up the good work!

Replay
Your next lesson will play in 10 seconds
• 0:00 Steps to Solve
• 2:00 Checking Your Work
• 4:04 Lesson Summary
Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Timeline
Autoplay
Autoplay
Speed Speed

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

So you want to learn how to solve the derivative of cos(2x). This lesson will do just that. We will look at how to use the chain rule to find this derivative and also see how to check our work using integrals.

## Steps to Solve

We want to find the derivative of cos(2x). To do this, we will make use of the chain rule. The chain rule is a rule used in calculus to find derivatives of compositions of functions. As a reminder, a composition of functions is a function of a function.

Well, now we can look at our function cos(2x) a bit differently. Notice that if we let f(x) = cos(x) and g(x) = 2x, then f(g(x)) = cos(2x). We see that cos(2x) is actually a composition of functions. Ah-ha! That's why we will make use of the chain rule to find its derivative. Okay, if we're going to use this chain rule, it's probably a good idea to actually know what that rule is.

The chain rule for derivatives states that to take the derivative of a composition of functions f(g(x)), we multiply the derivative of f with g(x) plugged in by the derivative of g(x).

f(g(x)) = f ' (g(x)) * g ' (x).

Good news! We already saw how to view cos(2x) as a composition of functions. We simply let f(x) = cos(x) and g(x) = 2x, then f(g(x)) = cos(2x). Perfect! Now we know we can use the chain rule to find the derivative of cos(2x) by plugging it into our formula. The only other information we need is as follows:

1. The derivative of cos(x) is -sin(x).
2. The derivative of 2x is 2.

Okay, let's get to work!

f ' (g(x)) = f ' (2x) * g ' (x) = -sin(2x) * 2 = -2sin(2x)

Once we get all the information we need to find this derivative, we see that finding the derivative is actually quite simple. The derivative of cos(2x) is -2sin(2x).

## Checking Your Work

Alright, we've seen that finding the derivative of cos(2x) isn't so hard, but what if we want to make sure we have the right answer? More good news! To check our work, we can use integrals. Integrals are basically just derivatives in reverse. Finding the integral of a function f is the same as finding the function that f is the derivative of. We can relate integrals and derivatives in the following way.

To unlock this lesson you must be a Study.com Member.
Create your account

### Register to view this lesson

Are you a student or a teacher?

### Unlock Your Education

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!

Support