f (x) = 5x+7x^(23))

f^-1(-12) =
(f^-1)' (-12) =

g(x) = x^2-12x+54 for x is an element of [6, infinity)

g^-1(19) =
(g^-1)'(19) =

ok - you've posted a couple dozen of these differentiation problems. I've done several, and given pointers on others.

stop dumping your homework here. If you have a problem that's stumping you, show us where you get stuck, and don't post any more like it till you get things worked out, or at least show some work indicating you've tried. Stop mooching.