Newton's Law of Universal Gravitation states that the force F between two masses, m1 and m2, is given below, where G is a constant and d is the distance between the masses. Find an equation that gives an instantaneous rate of change of F with respect to d. (Assume m1 and m2 represent moving points.)

Explanation:

According to newton's law , force between mass m₁ and m₂ at distance x is given by the following expression

F = G m₁m₂ / x²

differentiating F with respect to x , we have

dF /  d x =  ₋2G m₁m₂ / x³ .

Rate of reduction  of force ∝  1 / x³

the force on the thing and the distance the force moves the thing