Suppose xy=-2 and dy/dt=-4. Find dx/dt when x=-1.

-2

Step-by-step explanation:

Dividing the given equation by x, we find y to be ...

y = - 2/x

Then ...

dy/dx = 2/x^2

and ...

dy/dt = (2/x^2) dx/dt

dx/dt = (x^2/2) dy/dt

When dy/dt = - 4 and x=-1, this is ...

dx/dt = (-1) ^2/2 (-4) = (1/2) (-4)

dx/dt = - 2