Question

If xy + x = 12 and dx/dt = -3, then what is dy/dt when x = 2 and y = 5?

Answer 1

If $xy + x = 12$, then
$\dfrac{d}{dt}(xy+x)= \dfrac{d}{dt}(12)$.
Use the chain rule:
$y\dfrac{dx}{dt}+x \dfrac{dy}{dt}+ \dfrac{dx}{dt}=0$,
Since x=2, y=5, dx/dt = -3, then

$5\cdot (-3)+2\cdot \dfrac{dy}{dt}+(-3)=0, \\ 2\cdot \dfrac{dy}{dt}=18, \\ \dfrac{dy}{dt}=9$.