$($a$)$ Assume the equation x $=$ At$3+$ Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B$.($Use the following as necessary: L and T$,$ where L is the unit of length and T is the unit of time.$)$

$[$A$]=$

$[$B$]=$

$($b$)$ Determine the dimensions of the derivative

dx$/$dt $=3$At$2+$ B$.$

$($Use the following as necessary: L and T$,$ where L is the unit of length and T is the unit of time.$)$

$[$dx$/$dt$]=$