#### Answer

$f'(x) = (32t)(4t^2+7)^{-1/2} $

#### Work Step by Step

In order to derivate this function you have to apply the chain rule
Let's make an «u» substitution to make it easier
$u = 4t^2+7 $
$f(u) = 8u^{1/2}$
Derivate the function:
$f'(u) = 4u^{-1/2}u'$
Now let's find u'
$u' = 8t$
Then undo the substitution, simplify and get the answer:
$f'(x) = 4(8t)(4t^2+7)^{-1/2} $
$f'(x) = (32t)(4t^2+7)^{-1/2} $