[See Solution] Which (if any) of the following vector fields are conservative: F(x, y)=e^x y \vecimath+e^x+y \vecjmath F(x, y)=2 x cos y \vecimath-x^2 sin y


Question: Which (if any) of the following vector fields are conservative:

  1. \(\vec{F}(x, y)=e^{x y} \vec{\imath}+e^{x+y} \vec{\jmath}\)
  2. \(\vec{F}(x, y)=2 x \cos y \vec{\imath}-x^{2} \sin y \vec{\jmath}\)

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