Differentiation and Rate of Change

The video tutorial explains how to determine the rate of change of a particle's y-coordinate as it moves along a curve defined by x^2 y^2 = 16. Given that the x-coordinate changes at a constant rate of -2 units per minute, the tutorial uses the chain rule to derive an equation and solve for dy/dt when the particle is at the point (1, 4). The solution involves substituting known values into the derived equation and simplifying to find that dy/dt equals 8 units per minute.

What is the equation of the curve along which the particle moves?

• x^2 y^2 = 16

• x^2 + y^2 = 16

• x^2 - y^2 = 16

• x^2 y = 16

At what rate is the x-coordinate of the particle changing?

• 2 units per minute

• 4 units per minute

• -2 units per minute

• 0 units per minute

What mathematical technique is used to differentiate the equation with respect to time?

• Chain rule

• Product rule

• Power rule

• Quotient rule

What is the derivative of x^2 with respect to x?

• x

• 2x

• x^2

• 2

What is the derivative of y^2 with respect to y?

• y^2

• 2

• 2y

• y

What values are substituted for x and y in the differentiated equation?

• x = 2, y = 3

• x = 3, y = 2

• x = 1, y = 4

• x = 0, y = 5

What is the value of dx/dt given in the problem?

• -2

• -1

• 1

• 2

What is the simplified form of the equation after substituting the known values?

• 16 dy/dt = 128

• 2 dy/dt = 16

• 4 dy/dt = 32

• 8 dy/dt = 64

What is the rate of change of the y-coordinate, dy/dt?

• 10 units per minute

• 8 units per minute

• 6 units per minute

• 4 units per minute

In what units is the rate of change of the y-coordinate expressed?

• Units per day

• Units per second

• Units per minute

• Units per hour