Problem statement: If where , for prove that
This is my approach:
So
It seems I made an major error somewhere or I have conceptual problems.
Help me!
Thank you
Yes, you made an error in the calculation of the 2nd partials. Here's the situation: you have a function r(x,y,z) and a function u=f(r) (in your case 1/r). So you want the partials of u w.r.t. x , y and z. The first partial u_{x}=f'(r(x,y,z) times r_{x} is used correctly. But the second partial is:
, using the product rule.
If you do this (replacing occurrences of r) you get:
Similarly for the other 2nd partials. It is then easy to see that Laplace's equation is satisfied.