Final answer:
The rate of change of the gravitational force with respect to distance is found by differentiating the gravitational force equation, which is -2Gm1m2/r^3, indicating the force decreases as distance increases.
Step-by-step explanation:
The rate of change of the gravitational force with respect to distance r can be determined by differentiating the expression for the gravitational force f(r). According to Newton's law of universal gravitation, the force between two masses is given by F = Gm1m2/r^2, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the centers of the two masses. To find the rate of change of force with respect to r, you would take the derivative of F with respect to r, which yields dF/dr = -2Gm1m2/r^3. The negative sign indicates that the force decreases as the distance increases.