Arguments of all the potential energies

Question

Discuss the below:

Q1) Both the Coulomb law and gravitational forces lead to potential energies of the form U =  γ/x r1 - r2x, where  denotes kq1q2 in the case of the Coulomb force and - Gm1m2 for gravity, and r1 and r2 are the positions of the two particles. Show in detail that - ∫1U is the force on particle 1 and - ∫2U that on particle 2.

Q2) Write out the arguments of all the potential energies of the four-particle system in

U = Uint + Uext = (U12 + U13 + U14 + U23 + U24 + U34) + (U1_ext + U2_ext + U3_ext + U4_ext)

For instance U = U (r1, r2, .... , r4), whereas U34 = U34 (r3 - r4). Show in detail that the net force on particle 3 (for instance) is given by - ∫3U.