Problem #$3$:

Find the following derivative $($assuming that $r(t)$ is differentiable$).$

$\frac{d}{dt}[r^{\text{'}}(t)*(r^{\text{'}\text{'}}(t)r(t))]$

$($A$)r^{\text{'}}(t)*(r^{\text{'}\text{'}\text{'}}(t)r(t))$

$($B$)r^{\text{'}\text{'}\text{'}}(t)*(r(t)r^{\text{'}}(t))$

$($C$)r^{\text{'}\text{'}\text{'}}(t)*(r^{\text{'}}(t)r(t))$

$($D$)r^{\text{'}\text{'}}(t)*(r(t)r^{\text{'}\text{'}\text{'}}(t))$

$($E$)r^{\text{'}\text{'}\text{'}}(t)*(r(t)r^{\text{'}\text{'}}(t))$

$($F$)r^{\text{'}}(t)*(r(t)r^{\text{'}\text{'}\text{'}}(t))$

$($G$)r^{\text{'}\text{'}\text{'}}(t)*(r^{\text{'}\text{'}}(t)r(t))$

$($H$)r^{\text{'}\text{'}}(t)*(r^{\text{'}\text{'}\text{'}}(t)r(t))$