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Need help with the Chain Rule

  1. Mar 23, 2008 #1
    1. The problem statement, all variables and given/known data

    A: Write f(x) = [tex]\sqrt{5-x^{2}}[/tex] as a composite of two functions.

    B: Use the Chain Rule to find the derivative of f(x) = [tex]\sqrt{5-x^{2}}[/tex]

    2. Relevant equations

    Chain Rule:

    y`= [tex]\frac{dy}{du}[/tex] [tex]\frac{du}{dx}[/tex]

    3. The attempt at a solution

    A:

    y = [tex]\sqrt{u}[/tex]
    u = 5 - x[tex]^{2}[/tex]


    B:

    This is where I get confused. I don't understand what's meant by "d" and what's meant by "y", "u", and "x".

    I know the two du's cancel out in the Chain Rule so you're left with:

    y`= (dy)(dx)

    Does this mean the derivative of y times the derivative of x? And if so, how do you know what y and x are?
     
  2. jcsd
  3. Mar 23, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Good!
    dy/dx is just notation for: take the derivative of the function y with respect to the variable x.

    Not exactly. y' = dy/dx.

    The point is that you want to find dy/dx and that dy/dx = (dy/du)*(du/dx). And it's easy to calculate the derivatives dy/du and du/dx.
     
  4. Mar 23, 2008 #3
    Thanks. That cleared the confusion. :cool:
     
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