Let $f(x)=\log(x)$ (the natural logarithm). I'm asked to find a system in $f', f'', f^{(3)}, f^{(4)}$ and use induction to prove my system is correct.
Edit: After the comments I now have the system $f^{(n)}=(-1)^{n+1}\cdot (n-1)! \cdot x^{-n}$
I proved the induction start (obviously since I found a system being true in the beginning), but can't do the induction step - is the guess correct? Could you provide me with some tip to do the induction step?
Thanks