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Can someone please help me in understanding why the following equation is true?

$[(r\frac{\partial}{\partial r})^2+ r\frac{\partial}{\partial r}] = \frac{\partial^2}{\partial r^2} + \frac{2}{r}\frac{\partial}{\partial r} = (\frac{1}{r}\frac{\partial}{\partial r}r)^2$

I understand how $(r\frac{\partial}{\partial r})^2 = r\frac{\partial}{\partial r} + r^2\frac{\partial^2}{\partial r^2}$, however, for the previous equation I am at a lost. Any help would be really appreciated.

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  • $\begingroup$ How did you get the second one. $\endgroup$ – Pranita Gupta Jan 11 at 9:41
  • $\begingroup$ The simplest way to verify is to apply it to a function, i.e. (r d/dr)^2 f(r). $\endgroup$ – lastgunslinger Jan 11 at 9:46
  • $\begingroup$ Apply it on f(r)/r and rf(r). $\endgroup$ – Pranita Gupta Jan 11 at 12:38

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