Question: Given

\[\begin{aligned} & x\left( t \right)=\left( {{e}^{t}},\ln t,{{t}^{2}} \right) \\ & y\left( t \right)=\left( \sin t,t,4 \right) \\ \end{aligned}\]

find

\[\frac{d}{dt}\left[ x\left( t \right)\times y\left( t \right) \right]\]