# with sample problems

## Intro

In business calculus, the Constant Rule is used to find the derivatives of constant functions, which are functions without variables (letters). In other words, a constant function is a function that is equal to a number.

## When to use

The constant rule is used to differentiate constant functions. Here's an example of a constant function:

$$f(x) = 5$$

We know this is a constant function because $f(x)$ is equal to a number. Because $f(x)$ equals $5$, this means that no matter what we plug into $f(x)$, the result will always be $5$:

$$f(2) = 5$$

$$f(234) = 5$$

$$f(1,000,000) = 5$$

$$f(-2.4) = 5$$

The result is always $5$. So the function is never changing, and for that reason, the derivative, which measures how a function is changing, is $0$.

## How to apply

Again, it's very straightforward: the derivative equals $0$ when the function is constant.

## Learn the concept

In words: The derivative of a constant function is always $0$

In math notation: When $f(x) = a$, and $a$ is a number, then $f'(x) = 0$

Let's examine a sample problem below.

## Sample problem

Given that $f(x)=17$,

Question 1Find $f'(x)$

Because $f(x)$ is a constant function, then its derivative is zero:

$$f'(x)=0$$

## Lesson review

• The Constant Rule is used to find the derivative of a constant function
• A constant function is a function that's composed of only a number (no letters)
• The derivative of a constant function is always $0$

Our 25-problem business calculus practice guide is coming spring 2017. Get on the list!