Question

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

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

solve
\[x'(t)y+y'(t)x=0\] which is now
\[10\times \frac{1}{2}+y'\times 8=0\] for \(y'\)

Answer 6

oh okay

Answer 7

thanks!

Answer 8

yw