Given that g is the inverse function of f, and f(3)=4, and f'(3)=5, then g'(4) =

The derivative of the inverse function is given by :

g'(x) = 1 / [ f ' (g (x) ) ]

Note that ( 3, 4) is on " f " so (4, 3) is on " g " so.....g (4) = 3

So

g ' ( 4) = 1 / [ f ' ( g (4) ) ] = 1 / [ f ' (3) ] = 1 / [ 5 ] = 1 / 5