Calculate derivative using central differencing

dx = 0.01;
x = 0:dx:2*pi;
signal = sin(x).*cos(10*x);
dsignaldx_true = cos(x).*cos(10*x) - 10*sin(x).*sin(10*x);

dsignaldx_forward = ForwardO1(signal, x);

dsignaldx_central = 
for i =  
    
end

error_forward_max = max(abs(dsignaldx_forward(2:end-1) - dsignaldx_true(2:end-1)));
fprintf('The maximum relative error encountered when using forward differencing with O(dx) error is %f\n', error_forward_max)

error_central_max = 
fprintf('The maximum error encountered when using central differencing with O(dx^2) error is %f\n', error_central_max)

error_forward_average = mean(abs(dsignaldx_forward(2:end-1) - dsignaldx_true(2:end-1)));
fprintf('The average error encountered when using forward differencing with O(dx) error is %f\n', error_forward_average)

error_central_average = 
fprintf('The average error encountered when using central differencing with O(dx^2) error is %f\n', error_central_average)

Answer 1

[KALYAN ACHARJYA]

Is this?

dx=0.01;
x=0:dx:2*pi;
signal=sin(x).*cos(10*x);
diff_cen=(sin(x+dx).*cos(10*(x+dx))-sin(x).*cos(10*x))/(2*dx);
diff_cen

# I hope, rest you will do

[Kyle Lazaroff]

dx = 0.01;
x = 0:dx:2*pi;
signal = sin(x).*cos(10*x);
dsignaldx_true = cos(x).*cos(10*x) - 10*sin(x).*sin(10*x);

dsignaldx_forward = ForwardO1(signal, x);

dsignaldx_central = (sin(x+dx).*cos(10*(x+dx))-sin(x).*cos(10*x))/(2*dx);
dsignaldx_central(1) = NaN;
dsignaldx_central(length(dsignaldx_central)) = NaN;
for i = 2:length(dsignaldx_central)-1;
    dsignaldx_central(i) = (signal(i+1)-signal(i-1))/2*dx;    
end

error_forward_max = max(abs(dsignaldx_forward(2:end-1) - dsignaldx_true(2:end-1)));
fprintf('The maximum relative error encountered when using forward differencing with O(dx) error is %f\n', error_forward_max)

error_central_max = max(abs(dsignaldx_central(2:end-1) - dsignaldx_true(2:end-1)));
fprintf('The maximum error encountered when using central differencing with O(dx^2) error is %f\n', error_central_max)

error_forward_average = mean(abs(dsignaldx_forward(2:end-1) - dsignaldx_true(2:end-1)));
fprintf('The average error encountered when using forward differencing with O(dx) error is %f\n', error_forward_average)

error_central_average = mean(abs(dsignaldx_central(2:end-1) - dsignaldx_true(2:end-1)));
fprintf('The average error encountered when using central differencing with O(dx^2) error is %f\n', error_central_average)

this is what I have, but the central derivative and the max error are not correct. I'm not sure where the mistake is