I need some help in proving that [itex]\partial^2 V / \partial x^2[/itex] + [itex]\partial^2 V / \partial y^2[/itex] = 0 , when V = 1/2ln(x^2+y^2)
The Attempt at a Solution
For [itex]\partial V / \partial x[/itex] here's what I get: (1/x^2+y^2) *2x*1/2 = x * (x^2+y^2)^-1
and for [itex]\partial V / \partial y[/itex]
(x^2+y^2)^-1 *y ....
As you can see if i differentiate them once , I don't end up with any terms which may cancel each other to get zero..
what am I over looking ? PDE is new to me. I know we keep one variable constant in respect to other,etc..