​ What is the inverse of the function?

y = x^(x-1)     solve for 'x

log (y) = (x-1) log 3

 

log(y) /log 3 = (x-1)              Remember:   Switching log bases:   Logb(a) =  log(a) / log(b)

log3 (y) = x-1

log3(y) + 1 = x                    Now switch the y's and x's

y = log3(x) + 1

f'(x) = log3(x) + 1