# Proof involving divergence and gradients

1. Dec 15, 2011

### Rusty87

del^2($\Phi$^2)=( 2$\Phi$del^2)(2||grad$\Phi$||^2)

typing out my entire solution will take me ages so I'm going to verbally explain what i've done. I tried to work on the right side of the equation to compress it and make it equal to the left side. it just isnt working. I took the magnitude of the gradient, squared it and plugged that into the equation. Then I plugged the laplacian ino the equation. When I get to the end of the compressing process. I get to this an then I have no idea where to go from here:
2∂^2$\Phi$($\Phi$+1){(1/∂(x^2))+(1/∂(y^2))+(1/∂(z^2))

2. Dec 16, 2011

### nonequilibrium

Sorry can you please use the correct latex codes? It's a pain to read it.

For the del or grad operator, use \nabla

for (partial) differentiation, use \frac{ \partial^2 ... }{ \partial x^2}

or if the expressions substituted in the "..." is long, it's often prettier if one writes \frac{ \partial^2 }{ \partial x^2} \left( ... \right)