Please show all the steps and what theorems you used.

Let f(x) = In(x - 1). Find the first, second, third, fourth and n-th derivative of f. As well, use mathematical induction to prove the n-th derivative of f is correct. As part of your solution. briefly explain what is mathematical induction. Hint: recall the definition of factorial is r! = 1 . 2 .3.. (r - 1) . ..r where r is a non-negative integer, and by convention 0! = 1