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Related Rates Problems

  1. Sep 24, 2007 #1
    Let x & y be differentiable functions of t and let s = sqrt(x^2+y^2) be the distance between the points (x,0) and (0,y) in the xy-plane.

    How is ds/dt related to dx/dt if y is constant?

    So I attempted to implicitly take the derivatives of the changing rates.

    ds/dt= 1/(2sqrt(x^2+y^2)) times 2x dx/dt + 2y

    Which simplifies to

    ds/dt= x/(sqrt(x^2+y^2)) dx/dt + y/(sqrt(x^2+y^2))

    I'm guessing there is something I'm not understanding because he book shows an answer of ds/dt= x/(sqrt(x^2+y^2)) dx/dt

    So what y does the y disappear? Or what am I doing incorrectly?
  2. jcsd
  3. Sep 25, 2007 #2


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    Ummm. "if y is constant" says the problem. On such a path, dy/dt=0.
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