Question

Suppose that x=x(t) and y=y(t) are both functions of t. If y² x=1, and dy/dt=-5 when x=-3 and y=-2, what is dx/dt?

Answer 1

To find dx/dt, differentiate the given equation y^2 * x = 1 with respect to t. After substituting the given values, solve for dx/dt.

Step-by-step explanation:

To find dx/dt, we can differentiate the given equation y^2 * x = 1 with respect to t:

2y * dy/dt * x + y^2 * dx/dt = 0

Substituting the given values dy/dt = -5, x = -3, and y = -2:

2(-2)(-5)(-3) + (-2)^2 * dx/dt = 0

Simplifying, we get:

60 - 4 * dx/dt = 0

4 * dx/dt = 60

dx/dt = 60/4

Therefore, dx/dt = 15.