Question

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.

xy = 8
Find dy/dt, given x = 4 and dy/dt = 11.

Answer 1

To find dy/dt, we first need to find dx/dt by differentiating the given equation xy = 8 with respect to t. We are given x = 4 and dy/dt = 11. Substituting these values into the equation, we can solve for dx/dt.

Step-by-step explanation:

To find dy/dt, we first need to find dx/dt by differentiating the given equation xy = 8 with respect to t. Taking the derivative of both sides, we get:

(x(dy/dt) + y(dx/dt)) = 0

We are given x = 4 and dy/dt = 11. Substituting these values into the equation, we can solve for dx/dt:

(4(11) + y(dx/dt)) = 0

44 + y(dx/dt) = 0

y(dx/dt) = -44

Now, using the fact that xy = 8, we can substitute this into the equation:

-44 = -8(dx/dt)

dx/dt = 44/8 = 11/2 = 5.5

Therefore, the values of dy/dt and dx/dt are 11 and 5.5, respectively.