What is the correct order of operations for differentiating r^2 with 2/r*d/dr?

[timmo567]

as an example, say I am operating on r^2 with 2/r*d/dr :

do I differentiate r^2 first, then times by 2/r or times by 2/r and then differentiate. Confused as they give different answers

 

[CompuChip]

The operator works precisely as you would expect when you write it out. So
\left( \frac{2}{r} \frac{d}{dr} \right)(r^2) = \frac{2}{r} \left( \frac{d}{dr} r^2 \right).