The earth exerts a gravitational force of F (f) = (2.99x10^16) / r^2 newtons on an object with a mass of 75kg located r meters from the center of the earth. Find the rate of change of force with respect to distance.

Umm this should be in physics but F is proportional to 1/r^2 I am assuming you want to just take the derivative in respect to r of both sides of the equation

F = (2.99x10^16) / r^2

So you do that and you get

dF/dr = - 2 (2.99 * 10 ^16) / (r^3)

is this for calc class?