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Homework Help: Differentiate 1 over 2+x

  1. Jun 14, 2010 #1
    1. The problem statement, all variables and given/known data I have to differentiate using the long formula [f(x+h)-f(x)] / (h).


    2. Relevant equations

    f(x) = (1)/(2+x), x=2

    3. The attempt at a solution

    First I wrote [ (1/2+x+h) - (1/2+x) ] / (h). Then I created a common denominator in the numerator. I then made the bottom denominator a fraction.

    Code (Text):

    (2+x)-(2+x+h)     (1)
    ___________    x  __
    (2+x+h)(2+x)      (h)
    I subtracted common variables from the numerator and got.

    Code (Text):

       -(h)                (1)
    ________             x ___
    [(2+x+h)(2+x)]         (h)

    Then I got:

           -(1)
    _______________
    (2+x+h)(2+x)
    But as I expanded the numerator, I found that I couldn't get rid of the last h. What is the problem?

    Thank you.
     
    Last edited: Jun 14, 2010
  2. jcsd
  3. Jun 14, 2010 #2

    lanedance

    User Avatar
    Homework Helper

    i think you dropped a minus sign

    also remember h is tending to zero... so multiple out, then take the limit & you can cancel terms tending to zero
     
  4. Jun 14, 2010 #3

    lanedance

    User Avatar
    Homework Helper

    note you can write in tex (click on below to see the code)
    [tex]\frac{-1}{(2+x)(2+x+h)} = \frac{-1}{(2+x)^2+h(2+x))} [/tex]
     
  5. Jun 14, 2010 #4
    Thanks for the quick reply.

    That would mean the solution to this particular problem is [tex]- \frac{1}{16}?[/tex]
     
  6. Jun 14, 2010 #5

    HallsofIvy

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    Science Advisor

    Yes.
     
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