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

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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1\[xy=4\] 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 \[x'(t)y+y'(t)x=0\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1it is easy to write \(x'\) than \(\frac{dx}{dt}\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1now if \(x=8\) then since \(xy=4\) you know \(y=\frac{1}{2}\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1and you are told \(x'=10\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1solve \[x'(t)y+y'(t)x=0\] which is now \[10\times \frac{1}{2}+y'\times 8=0\] for \(y'\)
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