Finite Difference Approximations of the First Derivative of a Function

Derivatives of functions can be approximated by finite difference formulas. In this Demonstration, we compare the various difference approximations with the exact value.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The first derivative of a function is defined as
The simplest finite difference formulas for the first derivative of a function are:
(forward difference)
(central difference)
(backward difference)
Both forward and backward difference formulas have error , while the central difference formula has error .
In this Demonstration, we show the difference in values calculated from the three difference formulas and the exact value.
1. Does the true error increase proportionally with the step size, , for the forward and backward difference formulas?
2. Does the true error increase proportionally with the square of the step size, , for the central difference formula?
[1] A. A. Kaw, D. Nguyen, and E. E. Kalu, Numerical Methods with Applications. http://numericalmethods.eng.usf.edu/publications_book.html.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+