Evaluate the integral ${}_S(gradF)*dS,$ where $S$ is the portion of the surface of a sphere defined by $x^2{y}^2{z}^2=1$ and $xyz1,$ and where $F=r(ijk),r=33yj3zk.($Assume that the sphere is outward oriented so that the normal of $S$ has a positive $k$ component.$)$

$($Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

${}_S(gradF)*dS=$