del_x=0.01;

x_o=0;

x_f = 1;



n=(x_f-x_o)/del_x;

for i=1:n
    x(i)=(i-1)/n;
    f(i)=sin(2*pi*x(i));
end

plot(x,f)
hold on

df_dx(1)=2*pi
df_dx(n)=2*pi

for j=2:n-1
    dx(j)=(x(j+1)-x(j-1));
    df_dx(j)=(f(j+1)-f(j-1))/(dx(j));
end

plot (x,df_dx)