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
$F =$ $(GmM)\over r^2$
Where G is the gravitational constant and r is the distance between the bodies.
a. Find $dF\over dr$ and explain what it means
b. Suppose that it is known that the Earth attracts an object with a force that decreases at the rate of 2 N/km when r = 20,000km. How fast does this force change when r = 10,000km?
Part a:
Derivative is $dF\over dr$ = $−2GmMr^{−3}$
$dF\over dr$ describes how the force changes over a change of distance.
Part b:
Do I just plug in r and leave GmM alone?
Best Answer
It is not correct (nor fully simplified). Each of $m,M,G$ will be treated as a constant when you're taking the derivative with respect to $r$ (and $G$ actually is a constant), so the task is much simpler than you're making it.
In particular, the only thing to which we'll need to refer is the power rule. (Hint: $\frac1{r^2}=r^{-2}$.)