I'm working on a question for a problem set that has the following hint:(adsbygoogle = window.adsbygoogle || []).push({});

For any function A:

[itex]\frac{d^{2}A}{dr^{2}} + \frac{2}{r}\frac{dA}{dr} = \frac{1}{r^{2}}\frac{d}{dr}(r^{2} \frac{dA}{dr})[/itex]

I don't understand how this is true; this is how I try to show that both sides are equal but it doesn't work out...any help would be appreciated.

[itex]\frac{d^{2}A}{dr^{2}} + \frac{2}{r}\frac{dA}{dr} = \frac{1}{r^{2}}\frac{d}{dr}(r^{2} \frac{dA}{dr})[/itex]

[itex]\frac{d}{dr}\frac{dA}{dr} + \frac{2}{r}\frac{dA}{dr} = \frac{1}{r^{2}}\frac{d}{dr}(r^{2} \frac{dA}{dr})[/itex]

[itex](\frac{d}{dr} + \frac{2}{r}) \frac{dA}{dr} = \frac{1}{r^{2}}\frac{d}{dr}(r^{2} \frac{dA}{dr})[/itex]

[itex]\frac{d}{dr} + \frac{2}{r} = \frac{1}{r^{2}}\frac{d}{dr}(r^{2})[/itex]

[itex]\frac{d}{dr} + \frac{2}{r} = \frac{d}{dr}[/itex]

[itex] \frac{2}{r} = \frac{d}{dr} - \frac{d}{dr}[/itex]

[itex] \frac{2}{r} = 0[/itex]

This is only true if r [itex]\rightarrow[/itex] [itex]\infty[/itex]. I think I must be doing something wrong - can anyone please explain what I'm doing wrong and show me how the hint is a true statement? Thanks!

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# I can't believe the hint that is provided; can someone explain how it is true?

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