## Problem on determining if a vector field is conservative

Let $\mathbf{F}(x,y) = 2 x \log y \ \mathbf{i} + x^2 / y \ \mathbf{j}$. Is $\mathbf{F}(x,y)$ conservative?
• ## Solution

Recall that
We identify $u(x,y) = 2 x \log y$ and $v(x,y) = x^2 / y$.
Because $\partial_y u(x,y) = \partial_x v(x,y)$, $\mathbf{F}(x,y)$ is conservative.