Differentiate with respect to time t.Suppose 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?
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 . . .