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Implicit Differentiation w/ Composite Function

  1. Oct 31, 2009 #1
    1. The problem statement, all variables and given/known data

    Given the equation y= f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate decreases at 3 units/s. At that point, how fast is the y-coordinate of the object changing?

    3. The attempt at a solution

    Dy/dx = f ' (x) dx/dt

    Would that be the correct way to begin this problem? Then plug in 3 for dx/dt and 1/2 for f'(x)?

  2. jcsd
  3. Oct 31, 2009 #2


    Staff: Mentor

    Not quite.
    You have
    y = f(x), where both y and x are assumed (implicitly) to be functions of t. I could write this as y(t) = f(x(t)), which would make the dependence of y and x on t explicit

    dy/dt = d/dt(f(x(t)) = f'(x(t)) dx/dt
    Here I have used the chain rule.
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