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find the rate of change of the distance between the origin and a moving point on the graph of y=x^2+2 if ds/dt=5 centimeters per second.

  • calculus -

    I will assume you meant
    dx/dt = 5, or else the answer to your question is given

    s = √(x^2 + y^2)
    = (x^2 + (x^2+2)^2)^.5
    = (x^4 + 5x^2 + 4)^.5
    ds/dt = (1/2)(x^4 + 5x^2 + 4)(4x^3 + 10x)(dx/dt)

    so after you plug in the value, not much else can be done
    Something fishy about the question, was there an x value given?

  • calculus -

    forgot the exponent ... should say'

    ds/dt = (1/2)(x^4 + 5x^2 + 4)^(-1/2)(4x^3 + 10x)(dx/dt)

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