LaTeX
f\prime(x)\approx\frac{f(x+h)-f(x-h)}{2h}Variables
- Define all variables and the step size before use.
How to use this formula
Approximates a derivative with a symmetric second-order difference.
Important notes
- Check convergence and truncation assumptions.
Quick example
Apply the central difference derivative to a smooth test function and compare with a known result.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Check convergence and truncation assumptions.
- For the Central Difference Derivative, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- The iteration, step size, tolerance, and stopping rule must be suitable for the problem and the method must converge in the chosen region.
Worked example
Apply the central difference derivative to a smooth test function and compare with a known result.
Common mistakes
- When copying Central Difference Derivative, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Do not report a numerical approximation without a tolerance, convergence check, and an estimate of rounding or truncation error.
Continue the workflow
Use Central Difference Derivative in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
f\prime(x)\approx\frac{f(x+h)-f(x-h)}{2h}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Central Difference Derivative used for?
Approximates a derivative with a symmetric second-order difference.
Can I copy this formula as LaTeX?
Yes. Copy f\prime(x)\approx\frac{f(x+h)-f(x-h)}{2h} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.