Difference Quotient Calculator
Difference of quotient calculator works out Derivative and Notation from Expression f(x), Differentiate with respect to and Evaluate at (optional). The default figures on this page give derivative of 2 * x + h; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
4 steps
- f(x + h) = (x + h)^2
- f(x + h) - f(x) = 2 * h * x + h^2
- Divide by h: 2 * x + h
- Letting h → 0 gives the derivative 2 * x.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the difference of quotient calculator calculates
Differentiates an expression symbolically with the power, product, quotient and chain rules, evaluates the derivative at a point, and builds the difference quotient or the linear approximation.
How to use this difference of quotient calculator
Enter Expression f(x), Differentiate with respect to, Evaluate at (optional) and Step h (difference quotient only). Derivative updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Derivative, Notation and Derivative at the point.
The method follows OpenStax, Calculus Volume 1, chapter 3 (Derivatives): the power, product, quotient and chain rules, OpenStax, Calculus Volume 1, section 4.2: Linear approximations and differentials and NIST Digital Library of Mathematical Functions, chapter 4: Elementary Functions (derivative table).
What you can compare
Change one input at a time to see how it affects Derivative, Notation and Derivative at the point. The inputs you can vary are Expression f(x), Differentiate with respect to, Evaluate at (optional) and Step h (difference quotient only).
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How do you calculate the difference quotient?
Differentiates an expression symbolically with the power, product, quotient and chain rules, evaluates the derivative at a point, and builds the difference quotient or the linear approximation. Open “How this is worked out” beside the result to see each step for your own figures.
When would you use the difference quotient?
Differentiates an expression symbolically with the power, product, quotient and chain rules, evaluates the derivative at a point, and builds the difference quotient or the linear approximation. On the figures this page opens with — evaluate at (optional) 2 — the derivative is 2 * x + h. Put your own figures in their place and the working updates beside the result.
Can you provide me with an average difference calculator?
It needs Expression f(x), Differentiate with respect to, Evaluate at (optional) and Step h (difference quotient only). Nothing else is required, and the figures stay in your browser.
What information do I need for the difference of quotient calculator?
You need Expression f(x), Differentiate with respect to, Evaluate at (optional) and Step h (difference quotient only). The page opens with default figures that give derivative of 2 * x + h, so you can see the scale before entering your own.
What does this difference of quotient calculator show?
It shows Derivative, Notation, Derivative at the point, f at the point, Tangent line / linearisation and Linear approximation, with the working and any warnings for your entries.
Can I check how the difference of quotient calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.