$\backslash vec\{F\}(x,y)=(e^y\backslash sin\; x)\backslash vec\{i\}+(e^y\backslash cos\; x)\backslash vec\{j\}$

$\backslash vec\{F\}(x,y)=(y\backslash cos\; x-y)\backslash vec\{i\}+(\backslash sin\; x-x)\backslash vec\{j\}$

$\backslash vec\{F\}(x,y)=(y^3)\backslash vec\{i\}+(3xy^2+1)\backslash vec\{j\}$

$\backslash vec\{F\}(x,y)=(2xy+y^2)\backslash vec\{i\}+(x^2+2xy)\backslash vec\{j\}$