- #1
JPBenowitz
- 144
- 2
So I am trying to find the nth derivative of the curvature function:
\kappa(x) = \frac{f''(x)}{[1 + (f'(x))^2]^\frac{3}{2}}
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?
\kappa(x) = \frac{f''(x)}{[1 + (f'(x))^2]^\frac{3}{2}}
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?
