Let x and y be functions of time t such that the sum of x and twice y is constant. Which of the following equations describes the relationship between the rate of change of x with respect to time and the rate of change of y with respect to time?

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  b)  dx/dt = -2dy/dt

Step-by-step explanation:

We are given that ...

  x(t) +2y(t) = k

for some functions x(t) and y(t) and some constant k.

Differentiating with respect to time gives ...

  x'(t) +2y'(t) = 0

  x'(t) = -2y'(t) . . . . . subtract the y term

In the form used in the answer choices:

  dx/dt = -2dy/dt . . . . . matches choice B