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 $$\nabla . \nabla \Phi$$is 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...