Question

A function \[f(x)=log(x), x > 0\] is given.
Come with a good guess what \[d^n/dx^n\] is, when n is a natural number.
Proof that your guess is correct.

Answer 1

It would be easier if you can mention where you are stuck at ;)

Answer 2

f' = 1/x
f'' = -1/x^2
f''' = 1*2/x^3
Hence, f^n = (-1)^n-1 * n-1!/x^n