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..

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- Jan 10th 2011, 05:38 AMkjchauhanVector Differentiation
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.. - Jan 10th 2011, 06:30 AMsnowtea
Hint:

$\displaystyle \displaystyle \frac{\partial f(r)}{\partial x} = f'(r) \frac{\partial r}{\partial x} = f'(r)\frac{x}{r} $

$\displaystyle \displaystyle \frac{\partial^2 f(r)}{\partial^2 x} = \frac{\partial^2 f'(r)\frac{x}{r}}{\partial x} = f''(r)\frac{x^2}{r^2} + f'\frac{r^2 - x^2}{r^3}$. - Jan 10th 2011, 06:50 AMkjchauhan
- Jan 10th 2011, 06:52 AMsnowtea