Let $\mathbf{c}_1(t) = (e^{5t}, \sin(2t), t^3)$, and $\mathbf{c}_2(t) = (e^{3t}, \cos(4t), 3t^3)$

$\displaystyle \frac{d}{dt}\left[ \mathbf{c}_1(t) \cdot \mathbf{c}_2(t)\right] =$
$\displaystyle \frac{d}{dt}\left[ \mathbf{c}_1(t) \times \mathbf{c}_2(t)\right] =$ $\mathbf{i}\ +$
$\hspace{1.15in}$ $\mathbf{j}\ +$
$\hspace{1.15in}$ $\mathbf{k}$

Your overall score for this problem is