If a function f(x) is tabulated at a uniform interval h, then f(x0 + nh) = f(xn) = fn where n is an integer and x0 is any arbitrary value.
First Derivatives
Approximations to f′0, plus the order of the leading error term, are given below.
Centre Differences

Forward Differences

Backward Differences

Second Derivatives
Approximations to f″0, plus the order of the leading error term, are given below.
Centre Differences

Forward Differences

Backward Differences
