Posted by Jo on Tuesday, October 25, 2011 at 12:04am.
A particle is moving along the curve whose equation is (xy^3)/(1+y^2)= 8/5. Assume the xcoordinate is increasing at the rate of 6 units/second when the particle is at the point (1,2). At what rate is the ycoordinate of the point changing at that instant? Is it rising or falling?

Calculus  Steve, Tuesday, October 25, 2011 at 5:12am
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.
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