# How do I differentiate in MATLAB?

Many students ask me how do I do this or that in MATLAB.  So I thought why not have a small series of my next few blogs do that.  In this blog, I show you how to differentiate a function.

The MATLAB program link is here.

The HTML version of the MATLAB program is here.

___________________________________________

%% HOW DO I DO THAT IN MATLAB SERIES?
% In this series, I am answering questions that students have asked
% me about MATLAB.  Most of the questions relate to a mathematical
% procedure.

%% TOPIC
% How do I differentiate a function?

%% SUMMARY
% Language : Matlab 2008a
% Authors : Autar Kaw
% Mfile available at
% http://nm.mathforcollege.com/blog/differentiation.m
% Last Revised : March 21, 2009
% Abstract: This program shows you how to differentiate a given function

%% INTRODUCTION
clc
clear all
disp(‘ABSTRACT’)
disp(‘   This program shows you how to differentiate’)
disp(‘   a given function and then find its value’)
disp(‘   at a given point’)
disp(‘ ‘)
disp(‘AUTHOR’)
disp(‘   Autar K Kaw of https://autarkaw.wordpress.com&#8217;)
disp(‘ ‘)
disp(‘MFILE SOURCE’)
disp(‘   http://nm.mathforcollege.com/blog/differentiation.m&#8217;)
disp(‘ ‘)
disp(‘LAST REVISED’)
disp(‘   March 21, 2009’)
disp(‘ ‘)

%% INPUTS

% Differentiate 7 exp(3*x) once and find the value of the
% first derivative at x=0.5
% Define x as a symbol
syms x
% Defining the function to be differentiated
y=7*exp(3*x);
% Defining the point where you want to find the derivative
xx=0.5;

%% DISPLAYING INPUTS
disp(‘INPUTS’)
func=[‘  The function is to be differentiated is ‘ char(y)];
disp(func)
fprintf(‘  Value of x where you want to find the derivative, x= %g’,xx)
disp(‘  ‘)
disp(‘  ‘)

%% THE CODE
% Finding the derivative using the diff command
% Argument 1 is the function to be differentiated
% Argument 2 is the variable with respect to which the
%    function is to be differentiated – the independent variable
% Argument 3 is the order of derivative
dydx=diff(y,x,1);
% subs command substitues the value of x
dydx_val=subs(dydx,x,xx);
%% DISPLAYING OUTPUTS
disp(‘OUTPUTS’)
derivative_func=[‘  The derivative of function ‘ char(y) ‘ is ‘ char(dydx)];
disp(derivative_func)
fprintf(‘  Value of dydx at x=%g is =%g’,xx,dydx_val)
disp(‘  ‘)

______________________________________________________________________

This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.mathforcollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, and the YouTube video lectures available at http://nm.mathforcollege.com/videos

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## Author: Autar Kaw

Autar Kaw (http://autarkaw.com) is a Professor of Mechanical Engineering at the University of South Florida. He has been at USF since 1987, the same year in which he received his Ph. D. in Engineering Mechanics from Clemson University. He is a recipient of the 2012 U.S. Professor of the Year Award. With major funding from NSF, he is the principal and managing contributor in developing the multiple award-winning online open courseware for an undergraduate course in Numerical Methods. The OpenCourseWare (nm.MathForCollege.com) annually receives 1,000,000+ page views, 1,000,000+ views of the YouTube audiovisual lectures, and 150,000+ page views at the NumericalMethodsGuy blog. His current research interests include engineering education research methods, adaptive learning, open courseware, massive open online courses, flipped classrooms, and learning strategies. He has written four textbooks and 80 refereed technical papers, and his opinion editorials have appeared in the St. Petersburg Times and Tampa Tribune.

## 8 thoughts on “How do I differentiate in MATLAB?”

1. I enough understand if so many students ask how to get derivative a function using tool box of matlab, because matlab script for the differential commonly included or available in applications tool box. So, sometime students rather confuse when they would calculate even for drawing the graph of derivatif a function respect to it’s independent variable. I believe the scripts of finding derivative a function examplized at above are not only useful for all students at USF but also for my students at Physics Department of ITS Surabaya. Thanks for the above explanation.

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2. Thank you for the posting. It is quite useful to get the derivative using this code. But I wonder is it suitable for matrix differentiation as well? If not, is there any other function that I can use to get matrix differentiation?

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3. hina says:

hi.i want to know how i defrentiate and plot cos2x in matlab

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1. The links are for the program are in the blog!

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4. retha says:

what a great tutorial. it really saved my time. thanks!

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5. bhagya says:

but this syms is not supporting to transfer function (s=tf(‘s’)) i wanted find derivative of transfer function with respect to s
s=tf(‘s’)
f=4*exp(-2*s)/(s-1)
i want df at s=0.1

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