Answer
$g'(t) = -\dfrac{63}{2}t^2(7t^3-1)^{-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 = 7t^3-1 $
$g(u) = -3u^{1/2}$
Derivate the function:
$g'(u) = -\dfrac{3}{2}u^{-1/2}u'$
Now let's find u'
$u' = 21t^2$
Then undo the substitution, simplify and get the answer:
$g'(t) = -\dfrac{3}{2}(21t^2)(7t^3-1)^{-1/2} $
$g'(t) = -\dfrac{63}{2}t^2(7t^3-1)^{-1/2} $
