Hello, ZangQ!

Differentiate with respect to timeSuppose a particle is moving along a path described by: .y .= .x² / (x-4)²

At the point (3,9), the x-coordinate of the particle is decreasing at a rate of 2.4 cm/s.

At what rate is the y-coordinate of the particle changing?t.

dy/dt .= .[(x-4)²·2x - x²·2(x-4)] / (x-4)^4 * (dx/dt)

. . which simplifies to: .dy/dt .= .-8x/(x-4)³ (dx/dt)

We are given: .x = 3, .dx/dt = -2.4

. . Plug them in . . .