Taking a logarithmic derivative of a function

I have the following expression:

$\mathrm{log}(1-\frac{r}{{r}_{s}})$

which I would like to take the following derivative of (and where ${r}_{s}$ is a constant):

$\frac{d(\mathrm{log}(1-\frac{r}{{r}_{s}}))}{d\mathrm{log}(r)}$

What kind of strategies could I employ to find a solution?

I have the following expression:

$\mathrm{log}(1-\frac{r}{{r}_{s}})$

which I would like to take the following derivative of (and where ${r}_{s}$ is a constant):

$\frac{d(\mathrm{log}(1-\frac{r}{{r}_{s}}))}{d\mathrm{log}(r)}$

What kind of strategies could I employ to find a solution?