Numerical Differentiation

In many situations, given the discrete data set (x _i , f _i ); i = 1, 2, …, n, we are faced with the problem of determining the derivative of a function f with respect to x. The discrete data set (x _i , f _i ); i = 1,2, …, n may be from an experiment in which we have only determined values f _i at discrete locations x _i . In such a situation the value of a function f ∀x ≠ x _i ; i = 1, 2, …, n is not known. Secondly, we only have discrete data points. A function f(x) describing this data set is not known yet.