general formulation for 1/g(x) derivative

Question

Is there a general formulation for $\frac {d^n(g(x)^{-1})}{dx^n}$ ? Something like $$\frac {d^n(g(x)^{-1})}{dx^n} = \sum_{i=1}^{f(n)}\prod_{k=1}^{h(n)} ...$$

do yoo mean $1/g(x)$ or the inverse function $g^{-1}$? – alexjo Jan 14 '14 at 14:13 — alexjo, Jan 14 '14 at 14:13
1/g(x) (The inverse is $g^{-1}(x)$, if I'm not mistaken.) – Nuno Silveira Jan 14 '14 at 14:17 — Nuno Silveira, Jan 14 '14 at 14:17

score 2 · Accepted Answer · answered Jan 14 '14 at 14:13

2

It's just the formula of Faà di Bruno

enter image description here

with $f(x)=\frac{1}{x}$

answered Jan 14 '14 at 14:13

user127.0.0.1

7,267

thanks and may I add this link – Nuno Silveira Jan 14 '14 at 14:28

general formulation for 1/g(x) derivative

1 Answers1