Vector calculus. Divergent vector field.

carstensentyl
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I don't even know where to start this one. I can do all the other problems in the section, but this one makes no sense
 
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a). since you've done the other problems, you surely saw some gradients and divergences. The easiest way to do this is piece by piece. First take the gradient of f to get a vector field. Then simply apply div to this vector field to get the answer.

once you get this you will see the answer for part b
 
um just do what it says? what part are you having trouble with?
 
I agree with ice109- if the problem asks you to find "div grad f", I would recommend that you first find the grad of f and then the div of that! I am assuming that, since you were given a problem like this, you know what "div" and "grad" are.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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