Find $r^{\text{'}}(t),r^{\text{'}\text{'}}(t),r^{\text{'}}(t)*r^{\text{'}\text{'}}(t),$ and $r^{\text{'}}(t)r^{\text{'}\text{'}}(t).$

$r(t)=\frac{5}{2}{t}^{2}i-3tj\frac{1}{2}{t}^{3}k$

$($a$)r^{\text{'}}(t)$

$($b$)r^{\text{'}\text{'}}(t)$

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

$($d$)r^{\text{'}}(t)r^{-\text{'}}(t)$