The chain rule for related rates

Exercise and reference answers

Questions

1. Question

   If x = f(t) and y = g(t), then dy/dx equals

   Choices

   1. (dy/dt) × (dx/dt)
   2. (dy/dt) ÷ (dx/dt)
   3. dy/dt + dx/dt

   Correct choice

   (dy/dt) ÷ (dx/dt)

2. Question

   That formula requires

   Choices

   1. dy/dt ≠ 0
   2. t > 0
   3. dx/dt ≠ 0

   Correct choice

   dx/dt ≠ 0

3. Question

   dy/dx at x = x₀ is written

   Choices

   1. f ′(x₀)
   2. f(x₀)
   3. f ″(x₀)

   Correct choice

   f ′(x₀)

Explanation