Troubles on differentiation inside a function

Do you guys know how to differentiate a function inside a function?

I want to input a function, ask the code to differentiate it and use both function and its derivative in a loop.

function [zero] = newton_raphson (x0,precisao,funcao)
%Estimates the root of a function

syms x
f=funcao(x);
derivada=diff(f,x);

x(1)=x0;
erro=realmax;
i=1;

while erro > precisao
    x(i+1)=x(i)-f(x(i))/derivada(x(i));
    erro = abs (x(i+1)-x(i));
    i=i+1;
end
disp(['The estimate root is ' num2str(x(end)) ' with ' num2str(i) ' iteractions.'])
return

The error message when i enter "newton_raphson(2,10^-3, @(x) x+1): ??? Error using ==> mupadmex Error in MuPAD command: Index exceeds matrix dimensions.

Error in ==> sym.sym>sym.subsref at 1366
            B = mupadmex('mllib::subsref',A.s,inds{:});

Error in ==> newton_raphson at 16
    x(i+1)=x(i)-f(x(i))/derivada(x(i));

Thanks!

[Sargondjani]

you should give the error message

note that 'error' is a reserved matlab command, so you shouldnt use it.

[Ryan]

I'm guessing f isn't in a proper format for diff. What is "func"? What class is f? What does unique(f) return?

[Arthur]

Sorry, you guys. My variables are on portuguese, i tried to rename it on english to make it easier here, but it seems it just messed up. Code fixed as the original, with the message error.

Answer 1

[Walter Roberson]

deri=diff(f,x)  %differentiate against a variable

Caution: what results will be a symbolic function, but later you try to invoke it as if it is a numeric function in the line

x(i+1)=x(i)-f(x(i))/deri(x(i));

I suggest you examine matlabFunction()

[Arthur]

I tried, but still couldn't do it.

The code on the while loop is ok. I tested it removing the variable funcao and putting a function and its derivative on the code, below the loop like this:

while erro > precisao
    x(i+1)=x(i)-f(x(i))/derivada(x(i));
    erro = abs (x(i+1)-x(i));
    i=i+1;
end
disp(['The estimate root is ' num2str(x(end)) ' with ' num2str(i) ' iteractions.'])
return

function y=funcao(x);
y=x^2-2*x+1;
return

function y=derivada(x);
y=2*x-2;
return

Thank you for the attention.

[Walter Roberson]

derivada = matlabFunction( diff(f,x), x);

Otherwise derivada would be a symbolic variable and derivada(x(i)) would be an attempt to index that variable at index x(i). You cannot pass a value to a symbolic expression using (VALUE) notation.