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It's not the same as $\nabla f$ because you have $\vec F = (P,Q)$ (pretend this is vector notation which isn't showing up for me) and to find if $\vec F$ is conservative, we are taking $\frac{\partial P}{\partial y}$ and $\frac{\partial Q}{\partial x}$.

It's not the same as $\nabla f$ because you have $\vec F = (P,Q)$ (pretend this is vector notation which isn't showing up for me) and to find if $\vec F$ is conservative, we are taking $\frac{\partial P}{\partial y}$ and $\frac{\partial Q}{\partial x}$. Basically, use the same set up as $\nabla f$ and swap the $\partial x$ with the $\partial y$.