$(1$ point$)$ Determine $if$ the vector field

$F(x,y,z)=($:$-e^{x}sin(yz),-e^{x}cos(yz),-y{e}^{x}cos(yz)$:$)$

$is$ conservative.

curl$(F)=$

$1$

Therefore $F$

$A.Is$ conservative

$B.Is$ not conservative

$IfFis$ conservative find a function $f$ such that $F=$gradf. $If$ not write $"$ DNE $".$

$f=$