Question

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

Answer 1

-2

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