Answer
$\frac{dF}{dr} = \frac{-2GmM}{r^{3}}$
Work Step by Step
The formula can be written as: $$F = GmMr^{-2}$$
In this formula $GmM$ can be treated as a contant as only $r$ is changing. Thus:
$$\frac{dF}{dr} = -2GmMr^{-3}
= \frac{-2GmM}{r^{3}}$$