Demo 10.3.4

t,Dx = FNC.diffcheb(3,[-1,1]);
Dx

f = x -> x + exp(sin(4*x));
dfdx = x -> 1 + 4*exp(sin(4*x))*cos(4*x);
d2fdx2 = x -> 4*exp(sin(4*x))*(4*cos(4*x)^2-4*sin(4*x));

n = 5:5:70;
err1 = zeros(size(n));
err2 = zeros(size(n));
for (k,n) in enumerate(n)
    t,Dx,Dxx = FNC.diffcheb(n,[-1,1])
    y = f.(t)
    err1[k] = norm( dfdx.(t) - Dx*y, Inf )
    err2[k] = norm( d2fdx2.(t) - Dxx*y, Inf )
end

plot(n,[err1 err2],m=:o,label=[L"f'" L"f''"],
    xaxis=(L"n"), yaxis=(:log10,"max error"),
    title="Convergence of Chebyshev derivatives")