Given three or more equally-spaced points, we can find an interpolating polynomial passing through those points, find the 2nd, 3rd, or even higher derivative of that polynomial, and evaluate the derivative at a point to get an approximation of the derivative at that point.

# Background

Useful background for this topic includes:

# References

- Bradie, Section 6.2, Numerical Differentiation, Part II, p.443.
- Mathews, Section 6.2, Numerical Differentiation Formulas, p.339.
- Chapra, Section 23.1, High-accuracy Differentiation Formaulas, p.632.

# Interactive Maplet

To generate the formula for higher derivatives, select 2nd, 3rd, etc. instead of 1st in the third drop-down box.

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.