I have complete numerical data and would like to take derivative of the response. Also, the x variable is constant numerical value while y variable is changing. So which formulae to use for calculating 1st derivative.
First of all the question needs to be clear. Which variable is input and which variable is output. Since you have already mentioned x is a constant, it is not a variable as it is not varying.
There are two possibilities as per your question. Since Y is a variable and X is constant, either your "X" is a function of "Y" where the function is a constant function, that is X=f(Y) therefore, you can take differentiation w.r.to Y or your function Y=f(X,t) where X is fixed and Y varies with respect to time, here, you can take differentiation w.r.to t.
But, without observing the data or more details of the exact problem, we can't suggest anything.
If I understand your problem correctly, then the y-values are changing for the same value of x. Simply, x is then not a variable in the first place; x is not the right choice. dy/dx is simply out of question.
You may have to find another suitable real variable (say z) which determines the changing value of y. Then you can think of obtaining dy/dz. Or may be then dy/dx = dy/dz . dz/dx may yield something that you are expecting.
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