How to properly take derivative of discrete data ?

Taking derivative of discrete data requires some fitting and then using the b-form of the polynomial.

How to make a 'good' fit and properly take derivative? I am confused what is the right behavior of the derivative. Things change quite rapidly with small adjustments of the fitting scaps coefficient 0.09 in the example below.

The test.txt data is attached.

T = load('test.txt'); x = T(:,1); y=T(:,2)
pp22 = csaps(x,y,0.09);%some fit b-form
pp22val = ppval(pp22,x);
figure(1012)
plot(x,pp22val,x,y) %quality of fit
p_der202 = fnder(pp22,2);
y_prime22 = ppval(p_der202,x); % values

figure(101)
plot(x,y_prime22)

Answer 1

[Rohit Garud]

You can use the gradient() function in newer versions of matlab

dy_by_dx = gradient(y(:)) ./ gradient(x(:))