#### Answer

$y' = 2x^{3} - 3x -1$
$y''= 6x ^{2} -3$
$y''' = 12x$
$y'''' = 12$
$y''''' = 0$
(and all higher derivatives will also be 0)

#### Work Step by Step

$y = \frac{x^{4}}{2} -\frac{3x^{2}}{2} - x$
$y' = 2x^{3} - 3x -1$
$y''= 6x ^{2} -3$
$y''' = 12x$
$y'''' = 12$
$y''''' = 0$
(and all higher derivatives will also be 0)