How to Show Derivatives of 1/R for a 1D Charge Distribution?

[raintrek]

Homework Statement

(Lead into question:

"Assume that charges +q, -3q, 2q lie at positions -2a, 0, +2a along the x-axis respectively.")

I've calculated dipole/quadrupole moments about the origin as well as the exact potential at x=+10a, however I'm confused by this next part to the question:

Show that, for a 1 dimensional problem,

d(1/R) / dx = -1/x²

and

d²(1/R) / dx² = 2/x³

where R is the distance between a lab fixed point x and an arbitrary origin x0.

Can anyone suggest a method of tackling this??

 

[Shooting Star]

Show that, for a 1 dimensional problem,

d(1/R) / dx = -1/x²

and

d²(1/R) / dx² = 2/x³

where R is the distance between a lab fixed point x and an arbitrary origin x0.

Can anyone suggest a method of tackling this??

I am at a loss to understand what this has to do with charges.

R has been defined to be equal to x.

So, d/dx(1/R) = d/dx(1/x) = -1/x^2 etc.