Constant Rule Calculator

Published on: April 20, 2025
Final Answer: Free Full Steps: Plus

This Constant Rule Calculator helps you differentiate constants such as 5, 12, or -3. The constant rule says the derivative of any constant is 0.

Step-by-step method

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

Formula: This is the constant rule formula.

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

The constant rule says the derivative of any constant is 0 because a constant does not change as x changes.

Example 1:

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

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 - 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 - Apply the constant rule.

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

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

Final answer:

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

Example 2:

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

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 - 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 - 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:

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