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Numerical derivative of analytic function

version (2.82 KB) by Daniel Ennis
Calculate the numerical derivative of an analytic function with different methods.

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Updated 31 Mar 2016

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% This function returns the numerical derivative of an analytic function.
% Of special note, is the incorporation of the "complex step-derivative"
% approach which offers greatly improved derivative accuracy compared to
% forward and central difference approximations. This is especially germain
% when accuracy at the level of machine precision is a concern.
% This function was motivated by: authored by Michael Sherman
% -The function with no inputs generates the example used in the above link.
% -For more information see the following citation which is also found in the above link:
% --Martins JR, Sturdza P, and Alonso JJ
% The complex-step derivative approximation
% ACM Trans. Math. Softw. 29(3) (2003)
% SYNTAX: dfdx=deriv(f,x,h,method)
% INPUTS: f - A function a handle (eg f=@(x) sin(x))
% x - Interval over which f(x) is defined
% h - Derivative step-size
% method - Numerical methods used to compute derivative
% 'forward2' - Two point forward difference
% 'forward3' - Three point forward difference
% 'central2' - Two point central difference
% 'central4' - Four point central difference
% 'complex' - Complex step-derivative approximation
% OUTPUTS: dfdx - Numerical estimate of the derivative of f(x)
% DBE 2006.07.31

Cite As

Daniel Ennis (2020). Numerical derivative of analytic function (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (2)

I'm looking for a package that approximates derivatives for NUMERICALLY defined functions (not analytic) ..

I have two arrays:
x=0:0.5:10 , and fun= a vector that defines my function at each of those values of x.

Now I want the derivative of fun with respect to x at each value of x.

Does such a package exist ??

Sunil Arya

It is good for the biginers in matlab compuation


Update BSD License.

Minor fix of the "description."

MATLAB Release Compatibility
Created with R14SP3
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired: Adaptive Robust Numerical Differentiation