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mfirv401 mfirv401
  • 21-03-2017
  • Mathematics
Answered



Let

xy = 1

and let

\frac { dy }{ dt } = 3

Find \frac { dx }{ dt } when x = 3.

Verified Answer :

wizard123
wizard123 wizard123
  • 21-03-2017

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

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