Given the vector field vec$(F)(x,y,z)=2x{y}^3$vec$()-3y^2{z}^2$vec$()+4x^3$zvec$(k),$

$(a)$ Find the curlvec$(F)(x,y,z).(5$ points$)$

$(b)Is$ vec$(F)(x,y,z)$ conservative? Explain your answer. $(2\mathrm{.}5$ points$)$

$(c)$ Find divvec$(F)(x,y,z).(5$ points$)$

$(d)Is$ vec$(F)(x,y,z)$ divergence free? Explain your answer. $(2\mathrm{.}5$ points$)$