# Partial differential equation

## Homework Statement

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

## 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

## Answers and Replies

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

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