Find the Laplace transform of following functions:

$($a$)$ constant function, a$.$

$($b$)$ unit step function $($denoted by $S(t)).$

$($c$)$ shifted unit step function $($denoted by $S(t-)).$

$($d$)$ rectangular pulse function of magnitude $h.$

$($e$)$ exponential function, $e^{at}.$

$($f$)$ sine function, $sint.$

$($g$)$ derivative, $\frac{df}{dt}.$