For finding of the first and second derivatives of function
, given in equidistant points
(
(5) Removing brackets and considering, that
we’ll receive: . (6) Similarly, considering
we’ll receive: . (7)
In the same way if necessary, it is possible to calculate any order derivative of function. We’ll notice, that at calculation of derivatives in fixed point
It is possible to deduce also formulas of numerical differentiation based on Newton’s second interpolating formula [1].
Let – system of equidistant points with step and corresponding values of given function. Putting and replacing the function by Stirling’s interpolating polynomial, we’ll receive: (8) where for brevity of record the following designations are entered:
and so on. From (8) in view of that , follows: (9) . (10) |

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>> Formulas of numerical differentiaon