# 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:

## 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.

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