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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**