I've got to find the divergence of this force, $$ \mathbf F=\left(x^2+y^2+z^2\right)^n\left(x\hat e_x+y\hat e_y+z\hat e_z\right) $$ I would know how to do it if the $n$ superscript wasn't there. Any ideas on this one?
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$\begingroup$ Hint: For $y=f(x)^n$, $dy/dx=nf(x)^{n-1}(df/dx)$. You'll have to apply this a few times. $\endgroup$– Kyle KanosCommented Oct 1, 2014 at 14:36
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$\begingroup$ One of my faves: "Div, grad, curl, and all that," by Schey. $\endgroup$– Carl WitthoftCommented Oct 1, 2014 at 15:27
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1 Answer
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Just use the definition http://en.wikipedia.org/wiki/Divergence and the fact that $ x^{2}+y^{2}+z^{2}=r^{2}$ $\nabla\cdot F = r^{2n}+2nx^2r^{2(n-1)}+r^{2n}+2ny^2r^{2(n-1)}+r^{2n}+2nz^2r^{2(n-1)} = 3r^{2n}+2nr^{2n}$
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2$\begingroup$ We generally try to avoid giving a complete answer to homework problems here, because that doesn't help much toward the questioners learning the material that they're studying. Instead, it's better to just give enough of a hint that the questioners are able to solve their homework problems themselves. See meta.physics.stackexchange.com/questions/714/… $\endgroup$– Red ActCommented Oct 1, 2014 at 15:38