# Math Help - Differential problem

1. ## Differential problem

Newton's law of gravitation states that the force F of attraction between two particles having masses m and M is given by F = (gmM)/s^2 for a constant g and the distance s between the particles. If s = 20 cm, use differentials to approximate the change in s that will increase F by 10%

I can get the derivative as dF/dS = -2(gmM)/s^3 but I'm not sure where to go from there.

2. Originally Posted by bob14423
Newton's law of gravitation states that the force F of attraction between two particles having masses m and M is given by F = (gmM)/s^2 for a constant g and the distance s between the particles. If s = 20 cm, use differentials to approximate the change in s that will increase F by 10%

I can get the derivative as dF/dS = -2(gmM)/s^3 but I'm not sure where to go from there.
You are looking for $\Delta s$ such that:

$\frac{dF}{ds}\Delta s = 0.1 F$

note: $\frac{dF}{ds}=-\frac{2F}{s}$

RonL