so $log(x)$ has this graph:
[$log(x)$ Graph](https://i.stack.imgur.com/TRA7S.png)

and $\frac{1}{ln(x)}$has this graph: [$\frac{1}{ln(x)}$ Graph](https://i.stack.imgur.com/f8vIZ.png)

$\frac{1}{ln(x)}$ is the derivative of $log(x)$

My question is why does the graph of $\frac{1}{ln(x)}$ have a negative values, when all the $log(x)$ graph does is increase?