The chain rule and logarithms practice question 12

$g$ is a product whose second factor is $h$ applied to $x^{3}$. Which rules does that need, and why are $h$ and $h'$ given at 8 rather than at 2?

Product rule first: $g = u\cdot v$ with $u = x^{2}$ and $v = h(x^{3})$. Then the chain rule for $v'$.

$v'(x) = h'(x^{3})\cdot 3x^{2}$. At $x = 2$, $x^{3} = 8$, which is exactly where $h$ and $h'$ are known.