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Homework Help: Differentiation of tan^-1

  1. May 28, 2007 #1
    1. The problem statement, all variables and given/known data
    f(x) = tan^-1[(10000-200x)/(26x^2-2750x+77725)
    need to find f'(x)

    2. Relevant equations

    if f(x) = tan^-1 (x/a), then f'(x) = a/(a^2+ x^2)

    3. The attempt at a solution

    ok...the attempt im willing to do on my own, just needing help to get it in the form of x/a.
    preciate it. thx.
    Last edited: May 28, 2007
  2. jcsd
  3. May 28, 2007 #2

    matt grime

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    Why would you want to get it in that form? You know the chain rule, you know the derivative of tan^{-1}, and you can differentiate the expression inside your square brackets.
  4. May 28, 2007 #3

    Gib Z

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    Additional to what matt grime said, you need the quotient rule as well for the rational function that is the argument of the arctan.
  5. May 28, 2007 #4
    if f(x) = tan^-1[x/a], then f'(x) = [a/(a^2+x^2)]
    thats the only way i can think of going about it.
  6. May 29, 2007 #5


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    With that, you can easily do it with the chain rule.
  7. May 29, 2007 #6
    will do. thanks. = )
  8. May 30, 2007 #7


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    As an aside the following identity is occasionally handy:
    And brings your formula into line with danago's.
  9. Jun 3, 2007 #8


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    What?? We have to memorize complicated identities like that??:frown:
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