Let $u(t)=9t^{3}i+(t^2-7)j-4k$ and $v(t)=e^{t}i+8e^{-t}j-e^{8t}k.$ Compute the derivative $of$ the following function.

$u(t)*v(t)$

Select the correct choice below and fill $in$ the answer box$(es)to$ complete your choice.

$A.$ The derivative $is$ the scalar function

$B.$ The derivative $is$ the vector$-$valued function