roblem $7$: Consider a force field $F=(e^x+yx,\frac{x^2}{2}+y^3+cos(yz),\frac{ycos(yz)}{z}-\frac{sin(yz)}{z^2}+\frac{1}{z})$

$($a$)$ Show that the force is conservative and hence obtain its corresponding potential. $[8$ marks$]$

$($b$)$ Hence, calculate the work done by a particle traversing a path from a point $(0,0,1)$ to a point $(1,1,1).$

$[2$ marks$]$