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.
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 $0$.
Again, it's very straightforward: the derivative equals $0$ when the function is constant.
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.
Given that $f(x)=17$,
Question 1Find $f'(x)$
Because $f(x)$ is a constant function, then its derivative is zero: