Recall that a vector field F (x,y)=P(x,y),Q(x,y) is conservative if QxPy=0. I call the quantity QxPy the "2D scalar curl" of F , because it is similar to something called the "curl" of a vector field in 3D. (The proper use of the word "curl" is for a vector field in 3. ) Similarly, Mathematica will compute the 2D scalar curl with the command Curl. Let's try this... Is F (x,y)=2xysin(x),x2 2y conservative? Do this on paper, and then see if Curl[F[{x,y}],{x,y}] gives you the same result. Is this vector field conservative? If so, find a potential function f:2 satisfying f(0,0)=1