Proving \Phi = 1 / r satisfies \nabla^2\Phi=0 in Cartesian coordinates

[cloudone]

Homework Statement

Using Cartesian coordinates show that \Phi = 1 / r satisfies \nabla^2\Phi=0 for r not equals to 0.

Homework Equations

The Attempt at a Solution

I tried to let r = x+y+z, then \nabla \Phi = ( \frac{1}{r^2} , \frac{1}{r^2}, \frac{1}{r^2}), but \nabla . \nabla \Phiis obviously not zero

 

[phyzguy]

You didn't do the differentiation correctly. What is the partial derivative of 1/r with respect to x?

 

[Mmmm]

..and r^2=x^2+y^2+z^2 would work better too...