Determine whether F is conservative

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Homework Statement



F(x,y,z) = <2xy + ze^xz, x^2 +ze^yz, xe^xz + ye^yz + 2z>

Homework Equations





The Attempt at a Solution

f

I know how to find the partial of F(x,y) but I don't know how to do it for F(x,y,z). How do I do this?
 
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I got it now :)
 
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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