#### Answer

$s'(t) = \left(\dfrac{1215}{2}t^2\right)(3t^3-8)^{1/2}$

#### Work Step by Step

In order to derivate this function you have to apply the chain rule
Let's make a «u» substitution to make it easier
$u = 3t^3-8 $
$f(u) = 45u^{3/2}$
Derivate the function:
$s'(u) = \dfrac{135}{2}u^{1/2}u'$
Now let's find u'
$u' = 9t^2$
Then undo the substitution, simplify and get the answer:
$s'(t) = \dfrac{135}{2}(9t^2)(3t^3-8)^{1/2}$
$s'(t) = \left(\dfrac{1215}{2}t^2\right)(3t^3-8)^{1/2}$