Question

Let

xy = 1
and let
\frac { dy }{ dt } = 3
Find \frac { dx }{ dt } when x = 3.

Answer 1

Take implicit derivative using product rule.

`((dx)/(dt))y + x((dy)/(dt)) = 0`
Solve for dx/dt

`(dx)/(dt) = -( x)/(y)((dy)/(dt))`
Plug in given values. Note if x=3, then y must be 1/3 because xy=1

`(dx)/(dt) = -( 3)/((1/3))(3) \\ \\ (dx)/(dt) = -27`