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Homework Help: Differentiate with respect to x

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Differentiate with respect to x

    y = tan^(-1) x

    2. Relevant equations

    3. The attempt at a solution

    ANSWER in book:

    y = tan^(-1) x
    x = tan y
    dx/dy = sec^(2) y = (1 + x^2)
    dy/dx = 1 / (1 + x^2)

    How is it known that sec^(2) y = (1 + x^2)
    Does it follow from an identity?
  2. jcsd
  3. Jan 16, 2012 #2
    Have this sorted.

    It follows from the identity sin^2 (x) + cos^2 (x) = 1
  4. Jan 16, 2012 #3


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    Staff Emeritus
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    It follows from
    x = tan(y)​
    So that
    Then use the identity relating sec2 and tan2 , etc.
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