second derivative of the inverse function I know that the derivative of the inverse function of $f(x)$ is $g'(y) = \frac{1}{f'(x)}$
But how to derive the formula for the second derivative of g(y) knowing that $\left[\frac{1}{f(x)}\right]' = -\frac{f'(x)}{(f(x))^2}$ ?
I just started studying this chapter, so please try to be as simple as possible ;-)
Thank you.

Note that $y = f(x)$ and $x = g(y)$ in the formula $g'(y) = \frac{1}{f'(x)}$. Hence you can now write
$$
g'(y) = \frac{1}{f'(g(y))} \, .
$$
Now use the chain rule and the known formula for $g'(y)$. 
