Answer
$\displaystyle \left.\frac{dx}{dy}\right|_{x=2}=\frac{2}{7}$
Work Step by Step
$\displaystyle \frac{dx}{dy}=\frac{1}{(\frac{dy}{dx})},\qquad \frac{dy}{dx}\neq 0$
$\displaystyle \frac{dy}{dx}=\frac{d}{dx}[3x-2x^{-1}]=3-2(-x^{-2})=3+\frac{2}{x^{2}}$
$\displaystyle \left.\frac{dy}{dx}\right|_{x=2}=3+\frac{2}{4}=3+\frac{1}{2}=\frac{7}{2}$
$\displaystyle \left.\frac{dx}{dy}\right|_{x=2}=\frac{2}{7}$
