## candiwonderland 3 years ago i need to find dy/dt when x=8 and dx/dt=10 for xy=4

1. anonymous

$xy=4$ 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 $x'(t)y+y'(t)x=0$

2. anonymous

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

3. anonymous

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

4. anonymous

and you are told $$x'=10$$

5. anonymous

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

6. candiwonderland

oh okay

7. candiwonderland

thanks!

8. anonymous

yw