Change of the Del operator in two particle interactions

[vish22]

Change of the "Del" operator in two particle interactions

Ok,so John Taylor's Classical Mechanics has this small subtopic "energy interactions between 2 particles".And,in that,hes defined a "del1" operator as the vector differential operator with respect to particle 2 at the origin.Hence,the force on 1 due to 2 is just the negative vector gradient(using "del1") of the potential field of 2 as a position function of particle 1.And upon shifting the relative positions of these 2 particles in an arbitrary interial reference frame,he introduced the "del"2 operator and equated the force of particle 1 on 2 as just the negative of "del2" operator and the potential function wrt. the particle 1(which is not at origin now).In fact,I did not understand the last step at all.Could someone please explain?Thanks.

 

[bp_psy]

You should try doing problem 4.50, that is prove 4.81 for a function of one variable using the chain rule.Start with f(r) where r=x_2-x_1 and differentiate f(r) wrt x_2 and x_1