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?