What Is the Derivative of This Gravitational Potential Energy Function?

[dvvz2006]

Can someone please tell me the derivative of the following with respect to little 'r' where G is the gravitational constant (6.67x10^-11), Me is mass of Earth (5.98X10^24kg), Ms is mass of a spacecraft that has a mass of 1000kg and R which is the distance between the Earth and the moon (384400 x 10^3m). Thanks.

U = (-GMeMs)/(r) - (GMmMs)/(R-r)

 

[KoGs]

Can someone please tell me the derivative of the following with respect to little 'r' where G is the gravitational constant (6.67x10^-11), Me is mass of Earth (5.98X10^24kg), Ms is mass of a spacecraft that has a mass of 1000kg and R which is the distance between the Earth and the moon (384400 x 10^3m). Thanks.
U = (-GMeMs)/(r) - (GMmMs)/(R-r)

re-write your equation U = (-GMeMs)/(r) - (GMmMs)/(R-r) as:
U = (-GMeMs)(r^-1) - (GMmMs)[(R-r)^-1]
Then it is simply using the chain rule. For the first term: Multiply by the exponent, subtract the exponent by 1 to get the new exponent. Everything else is constant so no need to touch it.

For the 2nd term same thing, except do not forget u also must take the derivative of what is on the inside. Which is -1.