Find the curl of each vector field

Question

The second image is the work I have so far. I'm just wondering if I correctly calculated the curl of F

Answer 1

As mentioned in the comments, I think you've either misread the question or just had a small mistake by popping an $f$ symbol in your calculations.

What you have, is :

$$F(x,y,z) = x(x^2 + y^2)^{-1}j - y(x^2 + y^2)^{-1}i$$

The general argument and method is correct and you've carried out the determinant calculation correctly. Correct that $f$ thingy and it will be perfect !