# How do you differentiate y= 12(x^2-7)^(1/3)?

I would use the Chain Rule to deal with the ${\left(\right)}^{\frac{1}{3}}$:
$y ' = 12 \cdot \frac{1}{3} {\left({x}^{2} - 7\right)}^{\frac{1}{3} - 1} \cdot 2 x = 8 x {\left({x}^{2} - 7\right)}^{- \frac{2}{3}}$