f(x) = x^3 + x
h(x) is the inverse of f(x)
Find the derivative of h(2), step by step please.
Thanks in advance!
He is using the inverse function theorem,
$\displaystyle \left(f^{-1}\right)'(x) = \frac1{f'\left(f^{-1}(x)\right)}$,
which is indeed very well known. You should familiarize yourself with it.
To find $\displaystyle \left(f^{-1}\right)'(2)$, we want to know $\displaystyle f^{-1}(2)$. So we set $\displaystyle f(x) = 2\Rightarrow x=1$ so $\displaystyle f(1)=2\Rightarrow f^{-1}(2) = 1$. Now make the substitutions, and finish it.