Quantum Mechanics Operators

1. The problem statement, all variables and given/known data
Given that [itex] \hat{p} = -i\hbar (\frac{\partial}{\partial r} + \frac{1}{r}) [/itex], show that [itex] \hat{p}^2 = -\frac{\hbar^2}{r^2} \frac{\partial}{\partial r}(r^2 \frac{\partial}{\partial r}) [/itex]

2. Relevant equations


3. The attempt at a solution
I tried [itex]\hat{p}\hat{p} = -\hbar^2((\frac{\partial}{\partial r})^2 + \frac{1}{r} \frac{\partial}{\partial r} + \frac{\partial}{\partial r}\frac{1}{r} +\frac{1}{r^2}) [/itex].

This gave me [itex] -\hbar^2((\frac{\partial}{\partial r})^2 + \frac{1}{r} \frac{\partial}{\partial r} )[/itex] instead of the 2 / r factor I needed.


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