% compute f'(0.1) if f(x) = e^x sqrt(2+x)
format long g
exp(0.1).*(sqrt(2.1) + (1/2)/sqrt(2.1)) % exact
x=-1:.4:1;
f=exp(x).*sqrt(2+x);
p=polyfit(x,f,5);
pprime = p(1:end-1) .* [5 4 3 2 1];
polyval(pprime,0.1) % approximate

% solve 0 = u_x + e^x, u(-1) = 0
for N = [2 5 10 15]
    [D,x]=cheb(N);
    D=D(1:N,1:N);
    v=D\(-exp(x(1:N)));
    err = max(abs( [v; 0] - (exp(-1)-exp(x)) ))
end
xx = -1:0.01:1;
plot(x,[v; 0],'o',xx,exp(-1)-exp(xx))