Hi, my prob is find the most accurate 1st derivative of f(x)=exp(cos(x)) at x=1, with h=0.5,0.25,..,2^(-16). I calculate the 1st der. using 1st order central diff formula & trying to improve the accuracy using Richardson extrap. got incorrect result

clear; clc; format shortG
f = @(x) exp(cos(x)); df = @(x) -exp(cos(x))*sin(x);
x = 1; Truef1 = df(x); A = [];
h = 1/2;
while (h >= 2^-16)
    f1 = (f(x+h)-f(x-h))/(2*h);
    A = [A; h f1];
    h = h/2;
end
D(:,1) = A(:,2); E(:,1) = abs((Truef1-D(:,1))/Truef1);
for i = 1:16
    for j = 2:i
        D(i,j) = ((4^j)*D(i,j-1)-D(i-1,j-1))/(4^j-1);
        E(i,j) = abs((Truef1-D(i,j))/Truef1);
    end
end
disp(D); disp(E);
Order = (log(E(3,2))-log(E(2,2)))/(log(A(3,1))-log(A(2,1)))
loglog(A(:,1),E,'-');

[John D'Errico]

Please learn to use the {} Code button when you post code. As you have posted it, this is unreadable.

Select the block of code, then click on the "{} Code" button. I'll fix it once for you.