Variable Rule Notes

Published on: September 29, 2026

This Variable Rule Calculator differentiates x on its own, and shows the working line by line. Because x increases at exactly the same rate as itself, its derivative is one, which is the power rule with an exponent of one. It is the building block every other derivative of a polynomial leans on. Following the same pattern every time keeps this base case visible rather than assumed.

Step-by-step method

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

Formula:

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

Problem

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

Approach

Step-by-step method

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

Step 1

Step 1 - Set up the problem.

In this problem: We are given \(x\). This is just the variable \(x\).

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

Step 2

Step 2 - Write the variable rule formula.

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

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

Step 3

Step 3 - Apply the variable rule.

In this problem: Since the expression is \(x\), its derivative is \(1\).

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

Final Answer

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