Let $f$ and $g$ be the functions defined by $f(t) = 2t^{2}$ and $g(t) = t^{3}+6t$.

Determine $f'(t)$ and $g'(t)$.
$f'(t) =$
$g'(t) =$

Let $p(t) = 2t^{2} (t^{3}+6t)$ and observe that $p(t) = f(t) \cdot g(t)$. Rewrite the formula for $p$ by distributing the $2t^{2}$ term. Then, compute $p'(t)$ using the sum and constant multiple rules.
$p'(t) =$

True or False: $p'(t) = f'(t) \cdot g'(t)$