Constant Multiple Rule Calculator

Published on: April 20, 2025

This Constant Multiple Rule Calculator helps you differentiate expressions where a constant multiplies a function of x. The constant multiple rule is used when a fixed coefficient sits in front of a variable expression, and it is one of the main rules needed before solving larger derivative problems. The calculator shows the setup, formula, applying the rule, and final answer.

Step-by-step method

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

Formula: This is the constant multiple rule formula.

\frac{d}{dx}c·f(x)=c·\frac{d}{dx}f(x)

Example 1: Take the problem 3x.

\(f\left(x\right) = 3 x\)

Step 1 - Set up the problem.

In this problem: We are given 3x. Write it as the coefficient 3 multiplied by the variable part x.

\(f\left(x\right) = 3 x\)

Step 2 - Write the constant multiple rule formula.

In this problem: This rule says a constant coefficient can be moved outside the derivative.

\frac{d}{dx}c·f(x)=c·\frac{d}{dx}f(x)

Step 3 - Apply the constant multiple rule.

In this problem: Move 3 outside the derivative and leave x inside the derivative.

\frac{d}{dx}\(3 x\)=\(3\)·\frac{d}{dx}\(x\)

Final answer: The final answer is 3*d/dx(x).

\(3\)·\frac{d}{dx}\(x\)

Example 2: Take the problem 5x^2.

\(f\left(x\right) = 5 x^{2}\)

Step 1 - Set up the problem.

In this problem: We are given 5x^2. Write it as the coefficient 5 multiplied by the variable part x^2.

\(f\left(x\right) = 5 x^{2}\)

Step 2 - Write the constant multiple rule formula.

In this problem: This rule says a constant coefficient can be moved outside the derivative.

\frac{d}{dx}c·f(x)=c·\frac{d}{dx}f(x)

Step 3 - Apply the constant multiple rule.

In this problem: Move 5 outside the derivative and leave x^2 inside the derivative.

\frac{d}{dx}\(5 x^{2}\)=\(5\)·\frac{d}{dx}\(x^{2}\)

Final answer: The final answer is 5*d/dx(x^2).

\(5\)·\frac{d}{dx}\(x^{2}\)