Power Rule for Derivatives: Examples & Explanation

Power Rule for Derivatives: Examples & Explanation
Coming up next: Trigonometry: Sine and Cosine

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

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:00 What Is the Power Rule?
  • 0:26 A Few Examples
  • 2:02 Working with…
  • 3:35 Lesson Summary
Add to Add to Add to

Want to watch this again later?

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

Log in or Sign up


Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Kimberlee Davison

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

The power rule for derivatives is simply a quick and easy rule that helps you find the derivative of certain kinds of functions. In this lesson, you will learn the rule and view a variety of examples.

What Is the Power Rule?

The power rule in calculus is a fairly simple rule that helps you find the derivative of a variable raised to a power, such as: x^5, 2x^8, 3x^(-3) or 5x^(1/2). All you do is take the exponent, multiply it by the coefficient (the number in front of the x), and decrease the exponent by 1.

A Few Examples

Let's take a look at a few examples of the power rule in action.

Example 1

Our first example is y = 7x^5

Identify the power: 5

Multiply it by the coefficient: 5 x 7 = 35

Reduce the power by one: 4

You get dy / dx = 35x^4

Example 2

Here's another example: y = 12x^2

y = (2 x 12) x^(2-1) = 24x

Example 3

And our next example: y = x^1000

y = 1000x^999

The previous three examples have used positive integer exponents. The same rule works if your exponents are negative or fractional.

Example 4

Here's an example: y = 36x^(1/2)

y = (1/2)(36)x^(1/2 - 1) = 18x^(-1/2)

Example 5

Another example: y = 2x^(-3)

y = (-3)(2)x^(-3-1) = -6x^(-4)

Remember, in cases like this example, that one less than a negative number is a number even farther from zero. For example, one less than -3 is -4.

Working With Expressions Other Than Monomials

So far, you've just looked at monomials, expressions with only one term, like 5x. In algebra, you often encounter binomials, expressions with two terms, like 5x^4 + 2x, or trinomials, expressions with three terms, like 3x^2 - 2x + 6.

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.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

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!
Create An Account