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Homework Help: Tricky Derivative! - I need quick help

  1. Oct 18, 2005 #1
    I am faced with the function:
    [tex]f(x)=\frac{e^x(x^2+x+4)+e^{-x}(x^3-1)(x^8+1)}{(e^x+x^2+1)(x^6e^x+2)}[/tex]

    Can anyone think of a QUICK, EFFECTIVE way of finding the first derivative of this function, in simplified form??

    I have tried using the product/quotient laws, and I am now facing huge expanding! (The document is attached).
    I am assuming that this is a very ineffective way of finding the derivative, so then I tried another method...
    I used logarithmic differentiation, but I realized that in order to get it into simplified form I will have to do much factoring/expanding also.

    Then I thought, maybe using first principles would be easier? But I haven't tried that method yet. I'm assuming it will also consist of a lot of expanding.

    Without telling me to use "delta-epsilon" because I haven't learned that yet, how can I find this derivative?


    Thank you.
     

    Attached Files:

    Last edited by a moderator: Oct 18, 2005
  2. jcsd
  3. Oct 18, 2005 #2
    I would break it up and brute force it. I don't see any shortcuts.
     
  4. Oct 18, 2005 #3
    :eek:




    Anyone else?... Please......................
     
  5. Oct 18, 2005 #4

    Tom Mattson

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    I don't see anything that can be done to make this less painful.
     
  6. Oct 18, 2005 #5

    hotvette

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    You might (??) gain some simplicity by multiplying out all of the polynomials before plug-n-chug......
     
  7. Oct 18, 2005 #6
    I guess I will have to....
     
  8. Oct 19, 2005 #7
    sometimes don't you just want to hug maple :)
     
  9. Oct 19, 2005 #8
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