Take implicit derivative using product rule.
[tex](\frac{dx}{dt})y + x(\frac{dy}{dt}) = 0[/tex]
Solve for dx/dt
[tex]\frac{dx}{dt} = -\frac{ x}{y}(\frac{dy}{dt}) [/tex]
Plug in given values. Note if x=3, then y must be 1/3 because xy=1
[tex]\frac{dx}{dt} = -\frac{ 3}{(1/3)}(3) \\ \\ \frac{dx}{dt} = -27 [/tex]
