#### Answer

$J'(v)=1+u^{-2}+6u^{-4}$

#### Work Step by Step

$J(v)=(v^3-2v)(v^{-4}+v^{-2})$
Use the product rule.
$J'(v)=(v^3-2v)(-4v^{-5}-2v^{-3})+(v^{-4}+v^{-2})(3v^2-2)$
Distribute.
$J'(v)=-4v^{-2}-2+8v^{-4}+4v^{-2}+3v^{-2}-2v^{-4}+3-2v^{-2}$
Combine like terms.
$J'(v)=1+u^{-2}+6u^{-4}$