A little advice on using the chain rule for differentiation I must be a little rusty, but how would I evaluate the following: $$ \frac{d}{dr}\left(1-\frac{b(r)}{r}\right)^{-1} $$ My stickler is that $b$ is a function of $r$...

Apply power rule outside, then chain rule for ecpression inside bracket.

Then apply quotient rule on $\dfrac{b(r)}{r}$, then again chain rule on $b(r)$ $$\frac{d}{dr}\left(1-\frac{b(r)}{r}\right)^{-1} = -1\left(1-\frac{b(r)}{r}\right)^{-2}\cdot(-1)\cdot\left(\dfrac{r\cdot\dfrac{d}{dr}b-b(r)}{r^2}\right)$$

$$=\dfrac{r\cdot\dfrac{db}{dr}-b(r)}{(r-b(r))^2}$$