If $r(t)=u(t)v(t),$ where $u$ and $v$ are the vector functions given below, find $r^{\text{'}}(2).$

$u(2)=($:$4,3,-4$:$),u^{\text{'}}(2)=($:$5,0,1$:$),v(t)=($:$t,t^2,t^3$:$)$