Constant Rule for Business Calculus

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.

constant rule for business calculus

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 $0$

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