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Homework Help: Finding d^2y/dx^2 for a parametrized curve

  1. Mar 23, 2010 #1
    Find d2y/dx2 as a function of t if x = t - t2 and y = t - t3

    Ok, so this basically means we're going to take the second derivative of y with respect to t over the derivative of x with respect to t.

    So the second derivative of y would be.

    [2 - 6t + 6t2]/(1 - 2t)2

    Now, we just put that over the first derivative of x which is 1 - 2t so we get:

    [[2 - 6t + 6t2]/(1 - 2t)2]/(1 - 2t)

    =

    (2 - 6t + 6t2)/(1 - 2t)3

    Correct or incorrect?
     
  2. jcsd
  3. Mar 23, 2010 #2

    gabbagabbahey

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    Homework Helper
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    Why do you think this?

    [tex]\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{dy}{dx}\right)[/tex]

    Use the chain rule

    [tex]\frac{d}{dx}=\frac{dt}{dx}\frac{d}{dt}=\frac{1}{x'(t)}\frac{d}{dt}[/tex]
     
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