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Chain Rule Problem!

  1. Oct 23, 2005 #1
    I have the function:


    I need to find separate, smaller functions which will result in the composition of this function.

    I tried but all I ended up with was:

    Therefore, [tex]y=f(g(x))[/tex]

    However, this is obviously a very inefficient way of finding the composition of this function.

    Can anyone lead me in the right direction?
  2. jcsd
  3. Oct 23, 2005 #2


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    How about,
    [tex]f(g(x)) = \sqrt{x + \sqrt{x}}[/tex]
    [tex]g(f(g(x))) = \sqrt{x + \sqrt{x + \sqrt{x}}}[/tex]
  4. Oct 25, 2005 #3
    I don't see how that works, Fermat.


    [tex]f(g(x)) = \sqrt{\sqrt{x + \sqrt{x}}}[/tex]

    You are substituting [tex]g(x)[/tex] under the squareroot of [tex]f(x)[/tex].
  5. Oct 25, 2005 #4


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    If you're applying the chain rule, you'll always be going from the outside in. Can you
    clarify what you mean by "obviously inefficient"?
  6. Oct 25, 2005 #5
    It's inefficient because I'm splitting up my "big" function into a small function and another big function.

    Shouldn't my composition functions all be small, simple functions?

    Nothing like [tex]g(x)=x+\sqrt{x+\sqrt{x}}[/tex]
  7. Oct 25, 2005 #6
    Fermat......... how does what you told me to do work? I don't understand.
  8. Oct 25, 2005 #7
    I think your way works fine. I have tried but can't find a more elegant way to make the composite right now. You have a simple [tex]f(g(x))[/tex] composite. That's easy to take the derivative of.

    You could rewrite your g(x) as [tex]x + f(x+f(x))[/tex] if you wanted.
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