# Nth Derivative of Curvature

## Main Question or Discussion Point

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?