Derivative Calculator
Derivative Calculator works out Derivative and Notation from What to compute, Expression f(x) and Differentiate with respect to. The default figures on this page give derivative of 3 * x^2; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
2 steps
- f(x) = x^3
- d/dx = 3 * x^2
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the Derivative 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 Derivative Calculator
Enter What to compute, Expression f(x), Differentiate with respect to and Order of the derivative. Derivative updates as you type, and “Use a worked example” loads checked figures you can adjust. 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).
Power rule: d/dx x^3 at x = 2 example
With What to compute: derivative, Expression f(x): x^3, Differentiate with respect to: x, Order of the derivative: 1, the calculator returns Derivative: 3 * x^2, Derivative at the point: 12, f at the point: 8. This example is checked against an independent source in the test suite.
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 What to compute, Expression f(x), Differentiate with respect to, Order of the derivative, Evaluate at (optional) and Approximate f at (linearisation 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
Is there a calculator that can do derivatives?
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 3 * x². Put your own figures in their place and the working updates beside the result.
Can a TI-84 calculator do derivatives?
It needs What to compute, Expression f(x), Differentiate with respect to, Order of the derivative, Evaluate at (optional) and Approximate f at (linearisation only). Nothing else is required, and the figures stay in your browser.
How to calculate derivatives on a calculator?
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.
How do I calculate a derivative?
The result gives Derivative, Notation, Derivative at the point, f at the point, Tangent line / linearisation and Linear approximation, each labelled with its unit so the figure can be read on its own.
What information do I need for the Derivative Calculator?
You need What to compute, Expression f(x), Differentiate with respect to, Order of the derivative, Evaluate at (optional), Approximate f at (linearisation only), Step h (difference quotient only) and Values of the other variables. The page opens with default figures that give derivative of 3 * x^2, so you can see the scale before entering your own.
What does this Derivative 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.