For each of the given functions $f(x)$, find the derivative $\left(f^{-1}\right)'(c)$ at the given point $c$, first finding $a=f^{-1}(c)$.

a) $f(x)= 3 x + 8 x^{9}$; $c = -11$
$a$ =
$\left(f^{-1}\right)'(c)$ =

b) $f(x)= x^2 - 17 x + 83$ on the interval $[8.5,\infty)$; $c = 17$
$a$ =
$\left(f^{-1}\right)'(c)$ =