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

Mathematics

1 answer:

Nikitich [7]3 years ago

8 0

Answer:

-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

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