Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3 - Page 140: 14

$f'(x)=\sqrt[3] {-\frac{8}{27x^{4}}}$

$f(x)=\sqrt[3] \frac{8}{x}=2x^{-\frac{1}{3}}$ $f'(x)=2(-\frac{1}{3})x^{-\frac{1}{3}-1}$ $f'(x)=-\frac{2}{3}x^{-\frac{4}{3}}$ $f'(x)=-\frac{2}{3\sqrt[3] {x^{4}}}$ $f'(x)=\sqrt[3] {-\frac{8}{27x^{4}}}$