Variable Rule Calculator

Published on: April 20, 2025

This Variable Rule Calculator helps you differentiate the basic variable x. The variable rule is one of the first derivative rules used in calculus, and it is used inside larger problems whenever a term depends directly on x. The calculator shows the setup, formula, solve step, and final answer.

Step-by-step method

  1. Set up the problem.
  2. Write the variable rule formula.
  3. Solve using the variable rule.

Formula: This is the variable rule formula.

\frac{d}{dx}\(x\)=\(1\)

Example 1: Take the problem x.

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

Step 1 - Set up the problem.

In this problem: We are given x. This expression is exactly the variable being differentiated.

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

Step 2 - Write the variable rule formula.

In this problem: The variable rule says that the derivative of x with respect to x is 1.

\frac{d}{dx}\(x\)=\(1\)

Step 3 - Solve using the variable rule.

In this problem: Since x changes one-for-one with itself, the derivative is 1.

\(\frac{d}{dx}\left(x\right) = 1\)

Final answer: The final answer is 1.

\(f'\left(x\right) = 1\)