Spherically symmetric

1. Mar 11, 2017

Taylor_1989

1. The problem statement, all variables and given/known data
Hi guys, having problem trying to understand what this question wants.

the question I am stuck with is 7.3.
2. Relevant equations

3. The attempt at a solution
So for a) I converted to spherical co-ordinates:
$log(r^2sin^\theta cos^2\phi+r^2sin^2\theta sin^2\phi+r^2 cos^2\theta)$ which simplifies to $log(r^2)=2log(r)$
is this correct?

for b) I am not quite sure what it wants. Could someone please advise. Thanks in advance

2. Mar 11, 2017

blue_leaf77

You forgot the 1 inside the log argument.
You can try calculating its gradient $\nabla f(r)$ and then the directional derivative in an arbitrary direction perpendicular to the radial unit vector $\hat r$.

3. Mar 11, 2017

LCKurtz

@Taylor_1989 : What is your definition of a function being spherically symmetric?

4. Mar 12, 2017

Taylor_1989

@LCKurtz Well looking at the above function, wid the 1 in. It will have to go from the center of the axis because the way i see it each side about the center will have the same volume, but if you say move it to the left one side will have a larger volume that the other.

5. Mar 12, 2017

LCKurtz

You were asked to show a certain function is spherically symmetric. How can you expect to do that if you don't know what being spherically symmetric is? That should have been included in the homework template under "relevant equations", which you left blank. Look in your text, find the definition, and quote it here. Then we might be able to help you.