Calculating del(1/r) with Separation Vectors: How to Prove the Equation?

[boardbox]

Homework Statement

let R be the separation vector from (a,b,c) to (x,y,z) and r be the magnitude of R.
Show that: del(1/r) = -R/r^2

Homework Equations

del is the gradient operator

The Attempt at a Solution

The problem is that I keep getting a 3/2 power in the denominator when I calculate the left hand side.

r = sqrt((x-a)^2 + (y-b)^2 + (z-c)^2)

1/r = ((x-a)^2 + (y-b)^2 + (z-c)^2)^-0.5

del(1/r) = -R/[(x-a)^2 + (y-b)^2 + (z-c)^2]^(3/2)

 

[yungman]

We just had this two days ago:

https://www.physicsforums.com/showthread.php?t=365971

You have the equation wrong:

\nabla(\frac{1}{R})=-\frac{\hat{R}}{R^{2}}

 

[boardbox]

I see, you're right. I missed the hat on R in my text. Thanks.