Chebyshev spectral derivation with 16 nodes for $\,f(x)=e^{\,\text{sin}^{2}\,(x)+\cos(x)}\,$ defined in $\,[0,2\,\pi].\,$

Question

I'm making the following exercise in Matlab, and I'm having trouble expresing my result in $x\in[0,2\pi]$ not in $x\in[-1,1]$. I first done this (as shown below) in Gauss-Lobatto points, but I don't know how to transform everything to the original domain ($[0,2\pi]$). Any fix, comment or hint is welcome, thank you in advance!

Exercise with Matlab: Given the function $\,f(x)=e^{\,\text{sin}^{2}\,(x)+\cos(x)}\,$ defined in $\,[0,2\,\pi].\,$ Find the derivative of such function using Chebyshev spectral derivation with 16 nodes and find the error (using infinite norm).

These 3 matlab files I have done:

Nodos=16;

[x1,w1,df1,error1]=EjerunoCheby(Nodos);

 hold on

 plot(x1,w1','g',x1,df1,'*');

 error1;

 str1 = num2str(error1);

 str2= num2str(Nodos);

 title(['Chebyshev with ' str2 ' nodes. Error (infinite norm): ' str1])

 hold off 

%%%%%%%%%%%%%%%%%%%end of file 1%%%%%%%%%%%%%%%%%%%%%

function [x,DerCheby,df,error] = EjerunoCheby(N)

enteros=0:N;

x=cos(pi*enteros/N);

f=exp((sin(x)).*(sin(x))+cos(x));

D=MatrizD(N);

DerCheby=D*f';

df=f.*(2.*sin(x).*cos(x)-sin(x));

error=max(abs(DerCheby'-df));

%%%%%%%%%%%%%%%%%%%end of file 2%%%%%%%%%%%%%%%%%%%%%

function [D] = MatrizD(N)

nrows = N+1;

ncols = N+1;

enteros=0:N;

x=cos(pi*enteros/N);

v=-x./(2.*(1-x.*x));

D=diag(v);

D(1,1)=((2.*N*N+1)./6);

D(N+1,N+1)=-D(1,1);

cc=ones(length(x)-2,1);

c=[2;cc;2];

for i = 1:ncols

    for j = 1:nrows

        if i~= j

            D(i,j) = (c(i)/c(j))*(((-1)^(i+j))/(x(i)-x(j)));

        end

    end

end

%%%%%%%%%%%%%%%%%%%%%end of file 3%%%%%%%%%%%%%%%%%%%%%%%%%%