Is $\mathbf{F}(x,y) = \frac{1}{x+y} \mathbf{i} + \frac{1}{x+y} \mathbf{j}$ conservative? If so, find a $\phi(x,y)$ such that $\mathbf{F}(x,y) = \nabla \phi(x,y)$?
Solution
Determining if $\mathbf{F}(x,y)$ is conservative
We recall how to determine if a vector field is conservative: