# Chapter 2 - Derivatives - 2.5 The Chain Rule - 2.5 Exercises - Page 158: 12

$-\frac{2x}{3(x^2-1)^{\frac{4}{3}}}$

#### Work Step by Step

Original Expression: $\frac{1}{\sqrt[3](x^2-1)}$ $u = x^2-1$ $f(u) = \frac{1}{\sqrt[3] u} = u^{-\frac{1}{3}}$ Apply the chain rule: $f’(u)u’$ $f’(u) =-\frac{1}{3}(u)^{-\frac{4}{3}} 2x$ $f’(x) =-\frac{1}{3}(x^2-1)^{-\frac{4}{3}} 2x$ Simplify: $-\frac{2x}{3(x^2-1)^{\frac{4}{3}}}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.