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candiwonderland Group Title

i need to find dy/dt when x=8 and dx/dt=10 for xy=4

  • one year ago
  • one year ago

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  1. satellite73 Group Title
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    \[xy=4\] and i guess \(x=x(t)\) and \(y=y(t)\) i.e. they are both functions of \(t\) so via the product rule you get \[x'(t)y+y'(t)x=0\]

    • one year ago
  2. satellite73 Group Title
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    it is easy to write \(x'\) than \(\frac{dx}{dt}\)

    • one year ago
  3. satellite73 Group Title
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    now if \(x=8\) then since \(xy=4\) you know \(y=\frac{1}{2}\)

    • one year ago
  4. satellite73 Group Title
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    and you are told \(x'=10\)

    • one year ago
  5. satellite73 Group Title
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    solve \[x'(t)y+y'(t)x=0\] which is now \[10\times \frac{1}{2}+y'\times 8=0\] for \(y'\)

    • one year ago
  6. candiwonderland Group Title
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    oh okay

    • one year ago
  7. candiwonderland Group Title
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    thanks!

    • one year ago
  8. satellite73 Group Title
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    yw

    • one year ago
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