Let $c_1(t)=e^{2t}i+6sin(t)j+t^{3}k$ and $c_2(t)=e^{-2t}i+5cos(t)j-7t^{3}k.$

$(Enter$ your solution $as$ a single vector using the vector form $(,*).$ Use symbolic notation and fractions where needed.$)$

$\frac{d}{dt}[c_1(t)+c_2(t)]=$