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



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anonymous
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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
\[x'(t)y+y'(t)x=0\]

anonymous
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it is easy to write \(x'\) than \(\frac{dx}{dt}\)

anonymous
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now if \(x=8\) then since \(xy=4\) you know \(y=\frac{1}{2}\)

anonymous
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and you are told \(x'=10\)

anonymous
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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 \(y'\)

candiwonderland
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oh okay

candiwonderland
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thanks!

anonymous
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yw