Let $c_1(t)=e^{4t}i+7sin(t)j+t^{3}k$ and $c_2(t)=e^{-4t}i+2cos(t)j-10t^{3}k.$

Determine the components of the result, $a,b,$ and $c,$ where

$\frac{d}{dt}[c_1(t)c_2(t)]=(a,b,c)$

$($Express numbers in exact form. Use symbolic notation and fractions where needed. NOTE: this problem is computationally challenging.$)$

$$

Incorrect Answer

$b=\frac{(-5,-5(t-11),121{}^2+22(t-11))}{\text{C}\text{o}\text{m}\text{m}\text{a}\text{s}in\text{l}\text{a}\text{r}\text{g}\text{e}\text{n}\text{u}\text{m}\text{b}\text{e}\text{r}\text{s}\text{a}\text{r}\text{e}\text{n}\text{o}\text{t}\text{a}\text{c}\text{c}\text{e}\text{p}\text{t}\text{e}\text{d}}$

Incorrect Answer

$c=|(-5,\frac{55}{2},0)||$

Question Source: Rogawski $4$e Calculus Early Trahscendenfals