Please help me to solve this problem:
Prove that:
$\displaystyle \nabla^2 f(r) = f''(r) + \frac{2}{r}f'(r)$
Where $\displaystyle r^2=x^2+y^2+z^2$
Thanks in advance..
Hint:
$\displaystyle \displaystyle \frac{\partial f(r)}{\partial x} = f'(r) \frac{\partial r}{\partial x} = f'(r)\frac{x}{r} $
$\displaystyle \displaystyle \frac{\partial^2 f(r)}{\partial^2 x} = \frac{\partial^2 f'(r)\frac{x}{r}}{\partial x} = f''(r)\frac{x^2}{r^2} + f'\frac{r^2 - x^2}{r^3}$.