Is the vector field given by F(x,y) = (xi + yj) / (x^2 + y^2) conservative?

I'm trying to determine whether the vector field given by F(x,y) = (xi + yj)/(x^2 + y^2) is conservative. I let f(x,y) be a potential function such that f(x,y) = ln(x^2 + y^2) + K. So now I'm trying to find the gradient of f(x,y) so I can determine whether the gradient is equal to F(x,y) since then F(x,y) would be conservative. This is where I'm stuck.