Calculating Derivatives of Constant Functions

Instructor: David Karsner
In calculus, one of the primary tasks is to find the derivative of a function. Different types of functions require different techniques to find their derivative. This lesson will cover the simple process to find derivatives of constant functions.

Your Paycheck and the Derivative of a Constant Function

In college I had a job that started out paying me $8 an hour. Four years later, I was still making $8 an hour. The change of my pay at any point would have been zero. I was making exactly the same amount all four years. If you wanted to make my pay into a function, it would be y=8 (a constant function) and y stands for the amount per hour I was making. The change in my pay at any point of those four years would be zero. This is the derivative of that constant function:

A Constant Function
PayRaise

The Derivative of a Constant Function

To put it simply, the derivative of any constant function is zero.

A constant function in x is a polynomial that consists of some real number. It does not have a variable component to it. You could say the x has a degree of 0 or x0, which is typically not written.

Examples of Constant Functions

f(x)=4

f(x)=-2.3

f(x)=123,456

The derivative of a function with respect to x is denoted with d/dx. The derivative of a function is a measure of how quickly the function is changing at a point x. The value of the derivative of any constant function will be zero.

Examples of Derivatives of Constant Functions

d/dx 4=0

d/dx -2.3=0

d/dx 123,456=0

The process of finding the derivative of a constant function is simple; however, it will benefit you to see where that answer is coming from.

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
Support