Consider $F$ and $C$ below.

$F(x,y,z)=yz{e}^{xz}i+e^{xz}j+xy{e}^{xz}k,$

$C$:$r(t)=(t^2+3)i+(t^2-3)j+(t^2-4t)k,0t4$

$($a$)$ Find a function $f$ such that $F=$gradf.

$f(x,y,z)=$

$($b$)$ Use part $($a$)$ to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ along the given curve $C.$