Nth Derivative of Curvature

  • Thread starter JPBenowitz
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So I am trying to find the nth derivative of the curvature function:

[itex]\kappa(x)[/itex] = [itex]\frac{f''(x)}{[1 + (f'(x))^2]^\frac{3}{2}}[/itex]

Now, I could go about using Faa Di Bruno's formula but when I did I realized that I also have to use the Leibniz formula as a substitution for a term in the Faa Di Bruno formula. Once I did that low and behold I had to use Faa Di Bruno's formula again for a term in Leibniz formula... so on and so forth about two times again. Is there any easier route to go about finding the nth derivative?
 

Answers and Replies

  • #2
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Probably not. It is in itself a question with a messy answer.
 

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