Formulas of numerical differentiation
1. On a basis of Newton’s first interpolating formula
For finding of the first and second derivatives of function
Removing brackets and considering, that
we’ll receive:
Similarly, considering
we’ll receive:
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
х
as
It is possible to deduce also formulas of numerical differentiation based on Newton’s second interpolating formula [1].
2. On a basis of Newton’s second interpolating formula
Let
where for brevity of record the following designations are entered:
and so on.
From (8) in view of that
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