# How do you find the derivative of q(x) = (8x) ^(2/3) using the chain rule?

Oct 31, 2015

I found: $q ' \left(x\right) = \frac{8}{3 \sqrt[3]{x}}$
$q ' \left(x\right) = \textcolor{red}{\frac{2}{3} {\left(8 x\right)}^{\frac{2}{3} - 1}} \cdot \textcolor{b l u e}{8} =$
$= \frac{16}{3} {\left(8 x\right)}^{- \frac{1}{3}} =$
$= \frac{16}{3} \cdot \frac{1}{\sqrt[3]{8 x}} =$
$= \frac{16}{3} \cdot \frac{1}{2 \sqrt[3]{x}} = \frac{8}{3 \sqrt[3]{x}}$