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.