Finding The Rate of Change

Question

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 with respect to time and the rate of

change of with respect to time?

A) dx/dt=2dy/dt

B) dx/dt=-2dy/dt

C) 2dx/dt+dy/dt=0

D) dx/dt + 2dy/dt=K, where K is a function of t

Answer 1

Well x + 2y = k (constant)

differentiate through wrt t

dx/dt + 2 dy/dt = 0

so dx/dt -2 dy/dt (so B)