Post a New Question

Calculus

posted by .

A particle is moving along the curve whose equation is (xy^3)/(1+y^2)= 8/5. Assume the x-coordinate is increasing at the rate of 6 units/second when the particle is at the point (1,2). At what rate is the y-coordinate of the point changing at that instant? Is it rising or falling?

  • Calculus -

    Use implicit differentiation:

    xy^3 / (1+y^2) = 8/5

    (y^3 + 3xy^2 y')(1+y^2) - xy^3 (2yy') = 0

    It's all over (1+y^2)^2, but that can be ignored, since it's never 0.

    y'(3xy^2 + 3xy^4 - 2xy^4) = -y^3(1 + y^2)

    y' = -y^3 (1+y^2)/(3xy^2 + xy^4)

    = -y/x * (1+y^2)/(3 + y^2)

    Take it from there.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus 1

    A particle is moving along the curve y= 4 \sqrt{3 x + 1}. As the particle passes through the point (1, 8), its x-coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the …
  2. Calculus

    A particle is moving along the curve y = 2 √{3 x + 7}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to …
  3. Calculus

    A particle is moving along the curve y = 2 √{3 x + 7}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to …
  4. Calculus

    A particle is moving along the curve y = 2 √{3 x + 7}. As the particle passes through the point (3, 8), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to …
  5. calculus

    A particle is moving along the curve y=4((3x+1)^.5). As the particle passes through the point (5,16) its -coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin …
  6. calculus

    A particle is moving along the curve y=5sqrt(3x+1). As the particle passes through the point (5,20) its x-coordinate increases at a rate of 3 units per second. Find the rate of change of the distance from the particle to the origin …
  7. Calculus

    A particle is moving along the curve . As the particle passes through the point , its -coordinate increases at a rate of units per second. Find the rate of change of the distance from the particle to the origin at this instant.
  8. Calculus

    A particle is moving along the curve . As the particle passes through the point , its -coordinate increases at a rate of units per second. Find the rate of change of the distance from the particle to the origin at this instant.
  9. Calculus

    A particle is moving along the curve . As the particle passes through the point , its -coordinate increases at a rate of units per second. Find the rate of change of the distance from the particle to the origin at this instant.
  10. Calculus HELP

    A particle is moving along the curve y=5 sqrt (2x+6). As the particle passes through the point (5,20 , its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin …

More Similar Questions

Post a New Question