Constant Rule Notes

Published on: September 29, 2026

This Constant Rule Calculator differentiates a plain number, and shows the working line by line. A constant function never changes as x moves, so its rate of change is zero no matter how large the constant is. That is why the answer is always zero rather than the constant itself. Following the same pattern every time makes the reasoning behind a zero derivative explicit instead of memorised.

Step-by-step method

  1. Set up the problem.
  2. Write the constant rule formula.
  3. Apply the constant rule.

Formula:

\(\frac{d}{dx}c = 0\)
See Example 1 Hide Example 1

Problem

\(f\left(x\right) = 5\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the constant rule formula.
  3. Apply the constant rule.

Step 1

Step 1 - Set up the problem.

In this problem: We are given \(5\). This expression does not contain \(x\), so it is a constant.

\(f\left(x\right) = 5\)

Step 2

Step 2 - Write the constant rule formula.

In this problem: The constant rule says the derivative of any constant is \(0\).

\(\frac{d}{dx}c = 0\)

Step 3

Step 3 - Apply the constant rule.

In this problem: Since \(5\) is constant, its derivative is \(0\).

\(\frac{d}{dx}\left(5\right) = 0\)

Final Answer

\(f'\left(x\right) = 0\)
See Example 2 Hide Example 2

Problem

\(f\left(x\right) = \frac{7}{2}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the constant rule formula.
  3. Apply the constant rule.

Step 1

Step 1 - Set up the problem.

In this problem: We are given \(\frac{7}{2}\). This expression does not contain \(x\), so it is a constant.

\(f\left(x\right) = \frac{7}{2}\)

Step 2

Step 2 - Write the constant rule formula.

In this problem: The constant rule says the derivative of any constant is \(0\).

\(\frac{d}{dx}c = 0\)

Step 3

Step 3 - Apply the constant rule.

In this problem: Since \(\frac{7}{2}\) is constant, its derivative is \(0\).

\(\frac{d}{dx}\left(\frac{7}{2}\right) = 0\)

Final Answer

\(f'\left(x\right) = 0\)
See Example 3 Hide Example 3

Problem

\(f\left(x\right) = 9\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the constant rule formula.
  3. Apply the constant rule.

Step 1

Step 1 - Set up the problem.

In this problem: We are given \(9\). This expression does not contain \(x\), so it is a constant.

\(f\left(x\right) = 9\)

Step 2

Step 2 - Write the constant rule formula.

In this problem: The constant rule says the derivative of any constant is \(0\).

\(\frac{d}{dx}c = 0\)

Step 3

Step 3 - Apply the constant rule.

In this problem: Since \(9\) is constant, its derivative is \(0\).

\(\frac{d}{dx}\left(9\right) = 0\)

Final Answer

\(f'\left(x\right) = 0\)
See Example 4 Hide Example 4

Problem

\(f\left(x\right) = - \frac{5}{3}\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the constant rule formula.
  3. Apply the constant rule.

Step 1

Step 1 - Set up the problem.

In this problem: We are given \(- \frac{5}{3}\). This expression does not contain \(x\), so it is a constant.

\(f\left(x\right) = - \frac{5}{3}\)

Step 2

Step 2 - Write the constant rule formula.

In this problem: The constant rule says the derivative of any constant is \(0\).

\(\frac{d}{dx}c = 0\)

Step 3

Step 3 - Apply the constant rule.

In this problem: Since \(- \frac{5}{3}\) is constant, its derivative is \(0\).

\(\frac{d}{dx}\left(- \frac{5}{3}\right) = 0\)

Final Answer

\(f'\left(x\right) = 0\)