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