function [] = approxsinederiv(N)

% stepsize
   h = 2*pi/N;

% measurements of sine function
   x = [0:h:2*pi];
   y = sin(x);

% approximate derivatives
   yprime(2:N) = (y(3:N+1)-y(1:N-1))/(2*h);
   yprime(1) = (y(2)-y(N))/(2*h);
   yprime(N+1) = yprime(1);

% exact derivatives
   exact = cos(x);

   subplot(221)
   plot(x,y,'x')
   axis([0 2*pi -1 1])
   subplot(222)
   plot(x,exact,'x')
   axis([0 2*pi -1 1])
   subplot(223)
   plot(x,yprime,'x')
   axis([0 2*pi -1 1])
   subplot(224)
   plot(x,abs(exact-yprime),'x')
   v = axis;
   axis([0 2*pi v(3) v(4)])