Derivative of lnn/n

1. Apply the quotient rule, which is:

   $$\frac{d}{d n} \frac{f{\left(n \right)}}{g{\left(n \right)}} = \frac{- f{\left(n \right)} \frac{d}{d n} g{\left(n \right)} + g{\left(n \right)} \frac{d}{d n} f{\left(n \right)}}{g^{2}{\left(n \right)}}$$

   $f{\left(n \right)} = \log{\left(n \right)}$ and $g{\left(n \right)} = n$.

   To find $\frac{d}{d n} f{\left(n \right)}$:

   1. The derivative of $\log{\left(n \right)}$ is $\frac{1}{n}$.

   To find $\frac{d}{d n} g{\left(n \right)}$:

   1. Apply the power rule: $n$ goes to $1$

   Now plug in to the quotient rule:

   $\frac{1 - \log{\left(n \right)}}{n^{2}}$

The answer is:

$$\frac{1 - \log{\left(n \right)}}{n^{2}}$$