CAL 3 problem: Working on a divergence theorem question. I don't understand how the answer manual does something. The problem goes... vectors are i j k F= [sqrt(x^2 + y^2 + z^2)] (xi + yj + zk) over the region D: 1

Question

CAL 3 problem: Working on a divergence theorem question. I don't understand how the answer manual does something. The problem goes...
vectors are i j k

F= [sqrt(x^2 + y^2 + z^2)] (xi + yj + zk) over the region D: 1<= x^2 + y^2 + z^2 <=2.

i get divergence theorem (i think) but the way I went about it was to go through spherical coordinates and let rho=sqrt(x^2 + y^2 + z^2) ->F=rho(x)i + rho(y)j + rho(z)k.
then i find the partials wrt x,y,z and come to my roadblock. 
I get (x^2/rho), same for y and z but my answer manual comes to (x^2/rho) + rho. I don't know where the + rho comes from.

experimentx · Answer

$ F= \sqrt{x^2 + y^2 + z^2} (xi + yj + zk) $ over the region D:  $ 1<= x^2 + y^2 + z^2 <=2  $

anonymous · Answer

yes thats correct

experimentx · Answer

are you trying to take divergence in spherical coordinate system??

anonymous · Answer

yes

experimentx · Answer

http://mathworld.wolfram.com/images/equations/SphericalCoordinates/NumberedEquation7.gif this is going to be ugly!!

anonymous · Answer

even if there is another way to look at this problem, I would like to know how the answer manual gets these partials

anonymous · Answer

haha i hope not

experimentx · Answer

It's a concentric sphere

anonymous · Answer

k. my problem isnt with integrals or divergence theorem. I just need to know where the + rho in the partial derivatives comes from

experimentx · Answer

http://www.wolframalpha.com/input/?i=divergence+ [sqrt%28x^2+%2B+y^2+%2B+z^2%29x%2C+sqrt%28x^2+%2B+y^2+%2B+z^2%29y%2C+sqrt%28x^2+%2B+y^2+%2B+z^2%29z] The calculated divergence ... by wolfram alpha

anonymous · Answer

lol coding fail

experimentx · Answer

$ \rho $ is the radius of the shpere
$$ \rho = \sqrt{x^2 + y^2 + z^2 }$$

experimentx · Answer

and also what are you trying to calculate???
net flux through the volume??

anonymous · Answer

flux through volume, ya

experimentx · Answer

The best way to do is $\sqrt{x^2 + y^2 + z^2} (xi + yj + zk) =  |r|\vec r$
You can calculate $ \nabla. |r|\vec r  = 4 |r|$

anonymous · Answer

hmm ok i see that, thanks, but i know how to do divergence problems. i just want to know about the + rho part of the partials

experimentx · Answer

or try changing $$ dV = r^2 \sin\phi \;drd\phi d\theta$$ and integrate ... 
well best of luck!!!

anonymous · Answer

To other viewers: my problem hasn't been solved. experimentx didn't answer my question.