How to find the nth derivative of square root of a polynomial using forward or backward differences. f(x)=sqrt(a0+a1 x + a2 x^2+a3 x^3+...an x^n)

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TR RAO
TR RAO 2018-2-5
回答： Jim Riggs 2018-2-5
f(x)=sqrt(a0+a1 x + a2 x^2+a3 x^3+...an x^n+...) How to find the nth derivative of square root of a polynomial using forward or backward difference formulas
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Jan
Jan 2018-2-5
If you use forward and backward differences, the function is evaluated numerically. Then it does not matter if it is the square root of a polynomial. But you can calculate the derivative by pencil and paper also. Please post, what you have tried so far, because this might help to understand, what you want.
John D'Errico
John D'Errico 2018-2-5
What have you tried? If nothing, why not?
Since this looks like homework, making an effort will get you more help than if you just post a doit4me.
Do you know how to evaluate the polynomial? Can you take the square root? Surely you can find forward difference schemes on wikipedia.

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Jim Riggs
Jim Riggs 2018-2-5
See the attachment for numerical derivative formulas from my collection.

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