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Math Help - Most general form for calculating derivatives using limits.

  1. #1
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    Most general form for calculating derivatives using limits.

    Right now I am working on finding the most general form for calculating a derivative using limits.

    Right now I have:

    \lim_{h\rightarrow0} \frac{f(x+nh)-f(x-zh)}{h(n+z)} = f'(x)

    I need to incorporate this finite differencing expression into the above formula.

    \frac{-f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h)}{12h}

    The finite differencing expression is also equal to the derivative.

    Any help would be greatly appreciated. Thank you.
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  2. #2
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    I know it has something to do with weighted averages, but I can't wrap my head around it.
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  3. #3
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    I figured it out, if any of you are interested.

    If you set <br />
lim_{h\rightarrow0} \frac{f(x+nh)-f(x-zh)}{h(n+z)} = P, then P is the derivative.

    Using a weighted average and the finite differencing formula, the most general form for calculating a first derivative is:

    \sum_{i = 1}^{n}\frac{a_{i}P_{i}}{a_{i}}
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