Question

Assume that x = x(t) and y = y(t). Let y = x + 4 and dx/dt = 2 when x = 3. Find dy/dt when x = 3.

Answer 1

To find dy/dt, we need to differentiate y with respect to t using the chain rule. Since y = x + 4, we can substitute this expression into y. Given that dx/dt = 2 when x = 3, we can conclude that dy/dt = 2 when x = 3.

Step-by-step explanation:

To find dy/dt, we need to differentiate y with respect to t using the chain rule. Since y = x + 4, we can substitute this expression into y. So, y = x + 4 = x(t) + 4. Now, differentiating both sides with respect to t gives dy/dt = dx/dt. Given that dx/dt = 2 when x = 3, we can conclude that dy/dt = 2 when x = 3.