integral and derivatives of a function

trying to attain the integral and derivative of a function, and then plot the derivative

ya(x)=sin^3((2/(x+2))-3)

i saved the function as file a3

function [ya] = a3(x)
ya = (sin((2./(x+2))-3)).^3;
end

then on a seperate file my code is:

clc
clear
 
inta3=integral(@a3,0,5)
 
x=0:0.1:5
Ax=a3(x)
diffa3= diff(Ax)/x
 
figure
plot(x,Ax)
hold on
xlabel('X')
ylabel('Y')
title('Derivative of 3a')

in the command window it says this when i run the code:

Error using  / 
Matrix dimensions must agree.

Error in a4 (line 10)
diffa3= diff(Ax)/x
 

i think th integral part is fine its just the derivative part

Answer 1

[madhan ravi]

clc
clear
inta3=integral(@a3,0,5)
syms x  % requires symbolic toolbox
Ax=a3(x)
diffa3= diff(Ax)/x % remember diff(Ax) is one element lesser than x always!
figure
fplot(x,Ax,[0 5])
hold on
xlabel('X')
ylabel('Y')
title('Derivative of 3a')

function ya = a3(x)
ya = (sin((2./(x+2))-3)).^3;
end

[Chloe St John]

thank you , i also want to obtain the derivative in the range of 0<=x<=5 do you know how i do this ?

and i tried researching the syms x tool but still not sure why it is necessary

thank you for your help !

[madhan ravi]

as you can see syms (wasn't necessary though) was used because it gives the analytical form of the derivative thereby to your latter question the derivative can be plotted in the rage from 0 to 5

fplot(...,[0 5])
    %     ^^^^^----- denotes 0<=x<=5

Answer 2

[madhan ravi]

Your way , see https://www.mathworks.com/help/matlab/ref/diff.html#btw_sz6-1 :

clc
clear 
inta3=integral(@a3,0,5);
x=0:0.1:5
Ax=a3(x);
diffa3= diff(Ax)./0.01;
% missed it-----^ ^^^^----- should be the step size
 
figure
plot(x(1:numel(Ax)),Ax) % look here
hold on
xlabel('X')
ylabel('Y')
title('Derivative of 3a')

function ya = a3(x)
ya = (sin((2./(x+2))-3)).^3;
end