Suppose F(x,y)=xy and x=x(t) and y=y(t). If x(1)=(1)/(2),y(1)=(1)/(3), x(')(1)=2, and y(')(1)=-3, then (dF)/(dt) at t=1 is equal to ________.
1) -1
2) -(5)/(6)
3) 0
4) (5)/(6)
5) 1