How is this Differentiation Trick Manipulated in Calculus?

[Baggio]

I keep seeing this trick everywhere but I don't see how it is done.

how do we go from

\frac{1}{r^{2}}\frac{d}{dr}(r^{2}\frac{d \rho}{dr} [\latex]<br /> <br /> to<br /> <br /> \frac{1}{r} \frac{d^{2} \rhor}{dr^2{}}[\latex]&lt;br /&gt; &lt;br /&gt; Ugggh can&amp;#039;t get latex to work anyway it&amp;#039;s&lt;br /&gt; &lt;br /&gt; (1/r^2)(d/dr(r^2. dx/dr)&lt;br /&gt; &lt;br /&gt; how do we go from that to&lt;br /&gt; &lt;br /&gt; (1/r)(d/dr(r^2.d(xr)/dr))&lt;br /&gt; &lt;br /&gt; I know for sure that they&amp;#039;re equal I just don&amp;#039;t know how to manipulate it! :(&lt;br /&gt; &lt;br /&gt; Thanks

 

[dextercioby]

Use [ tex ] [ /tex ] (without the spaces).

\frac{1}{r^{2}}\left(2r\frac{d\rho}{dr}+r^{2}\frac{d^{2}\rho}{dr^{2}}\right)<br /> =\frac{2}{r}\frac{d\rho}{dr}+\frac{d^{2}\rho}{dr}

and u can see pretty clearly the 2 things are different.

Daniel.

 

[dextercioby]

Who's "x" and what does he do...?

Daniel.

 

[Baggio]

No, let's start again

(1/r^2)(d/dr(r^2. dx/dr)

&

(1/r)(d/dr(r^2.d(xr)/dr))

x is a function of r, if you expand both you get the same result, but how can I go directly from the top eq to the bottom