This problem has me stumped:(adsbygoogle = window.adsbygoogle || []).push({});

If [tex]r = (x^2 + y^2)^{1/2}[/tex], show that

[tex] div \left( \frac{h(r)}{r^2}(x \vec{i} + y \vec{j}) \right) = \frac{h'(r)}{r}[/tex]

My trouble is with mixing the polar coordinates with the position vector. If I write the above as

[tex] div \left( \frac{h((x^2 + y^2)^{1/2})}{(x^2 + y^2)}(x \vec{i} + y \vec{j}) \right) = \frac{h'((x^2 + y^2)^{1/2})}{(x^2 + y^2)^{1/2}}[/tex]

I can try to get from the left side to the right side by computing the partial derivatives, but when I started this it involved so much messy differentiation (double chain rule, quotient rule) that it just seemed like it wasn't the right approach, so I didn't even try it.

Buteven if I did, what would h' be if h is a function of two variables? I've never seent the notation f '(x,y), just directional derivatives and partials...

What I'm saying is, even if I did do all the messy differentiation and kept all my stuff in order, I don't see how I would be able to write an h'(r) in the end.

Where am I going off track?

Thanks.

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

Dismiss Notice

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: Divergence Problem

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