Newton's Law of Gravitation says that the magnitude $F$ of the force exerted by a body of mass $m$ on a body of mass $M$ is $\displaystyle F=\frac{GmM}{r^2}$, where $G$ is the gravitational constant and $r$ is the distance between the bodies.

(a) Find $dF/dr$. [What does the minus sign mean?]
(b) Suppose it is known that Earth attracts an object with a force that decreases at a rate of 2 N/km when $r=20000$ km. How fast does this force change when $r=10000$ km?

(a) $dF/dr=$
(b) N/km