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Derivative of Arc Secant

  1. Oct 17, 2006 #1
    Hello there

    In the derivative of the arc secant, why is the absolute value of x ( which is present in the denominator) taken? Is this to prevent the possible of having a zero ( and making the whole expression undefined ? )

  2. jcsd
  3. Oct 18, 2006 #2


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    Science Advisor

    No, absolute value won't do that: |0|= 0 so you still can have in the denominator. (And the derivative is undefined for x= 0.) Strictly speaking the inverse secant is only defined for x less than -1 or greater than 1. It is because of the square root in the derivative that we have a "plus or minus" which, combined with x itself, makes the derivative always positive.
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