Answer
$\displaystyle \left.\frac{dx}{dy}\right|_{x=1}=\frac{1}{4}$
Work Step by Step
$\displaystyle \frac{dx}{dy}=\frac{1}{(\frac{dy}{dx})},\qquad \frac{dy}{dx}\neq 0$
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}[3(2x)-2]=6x-2$
$\left.\frac{dy}{dx}\right|_{x=1}=6-2=4$
$\displaystyle \left.\frac{dx}{dy}\right|_{x=1}=\frac{1}{4}$
