\( n^\text{th} \) derivative?

Calculus Level 3

If \(n\) is a non-negative integer, find the \(n^\text{th} \) derivative of \( \dfrac{\ln x}x \).

\[\frac{ {(-1 }^{n}n!}{ {x}^{ n+1}} \left(\ln(x)-\sum _{ k=1 }^{ n }{ \frac { 1 }{ k } } \right)\] \[\ln(x)-x\] Cannot be determined \[\frac{{(-1)}^{n-1}n! }{{x}^{n}}\left (\ln(x-n)-\sum _{ k=1 }^{ n }{ \frac { 1 }{ k } } \right)\] \[x(\ln(x)-x) \]