\(\bf s(t)=tcos(\pi -4t)\\\\
-----------------------------\\\\
\cfrac{ds}{dt}[tcos(\pi -4t)]
\\\\\\
\begin{array}{llll}
\left[ 1\cdot cos(\pi -4t) \right]\quad +\quad &\left[t\cdot \underline{[-sin(\pi -4t)]\cdot (0-4)} \right]\\
&\qquad \qquad \uparrow \\
&\textit{the chain-rule applies}\\
&\textit{when taking the derivative}\\
&\textit{to the second term}\\
&\textit{in the product rule}
\end{array}
\\\\\\
\left[ cos(\pi -4t) \right]+\left[ 4tsin(\pi -4t) \right]\impliedby s'(t)\iff velocity\)
