Differentiation using diff command

Hi I am using diff command and in the end I need to compare the actual differential value with the one I am getting after using diff command, here is my code

Please tell me how can I get the correct value so as the relation can be built between the error and step size, i.e smaller the step size( or in other words greater the samples) smaller will be the error and results will get closer to the actual value my code is:

dt=0.01; %dt=1,0.1,0.01
t=0:dt:2*pi;
x=sin(t);
yt=cos(t);    %mathematical differential
dx=diff(x)./dt;
dx=[0;dx(:)]'% Making its length equal to the vector yt since we are padding a zero here it gives incorrect results
y_sum=sum(yt)
x_sum=sum(dx)
error=yt-dx;
sum_error=sum(error)

Because this code is giving me opposite results

[Walter Roberson]

When you calculate

y_sum=sum(yt)

you are approximating integral of cos(t) from t = 0 to t = 2 * pi, if you were multiplying by dt. But your dx has been divided by dt.

[hm]

oh yes thaaanks, but the worst part is sum of errors is where the error goes how can i get a relation between the two smaples and error