Let ${\bf r}(t) = \left< t^2,1-t,4 t \right>$. Calculate the derivative of ${\bf r}(t)\cdot {\bf a}(t)$ at $t=6$,
assuming that ${\bf a}(6) = \left< -6 , 5 , 9 \right>$ and ${\bf a}'(6) = \left< 1 , -5 , 4 \right>$

${\displaystyle \frac{\,d}{\,dt} {\bf r}(t)\cdot {\bf a}(t)|_{t=6} =}$