$9-16.$ Testing for conservative vector fields Determine whether the following vector fields are conservative $($in $R^2$ or $R^3).$

$9.F=($:$1,1$:$)$

$10.F-(x,y)$

$11.F=($:$-y,x$:$)$

$12.F=($:$-y,xy$:$)$

$13.F=(e^{-x}cosy,e^{-x}siny)$