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Derivative of inverse trig function absolute value?

  1. Apr 14, 2013 #1
    Find the derivative of y = arctan(x^(1/2)).

    Using the fact that the derivative of arctanx = 1/(1+x^2) I got:

    dy/dx = 1/(1+abs(x)) * (1/2)x^(-1/2)

    But my textbook gives it without the absolute value sign. I don't understand why because surely x^(1/2) squared is the absolute value of x and not simply x?
     
  2. jcsd
  3. Apr 14, 2013 #2

    mfb

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    x^(1/2) is well-defined for positive x only (unless you work with complex numbers). If you don't have any negative numbers, ...
     
  4. Apr 14, 2013 #3
    you have to consider the signs of the trigo identities
     
  5. Apr 14, 2013 #4
    Oh okay. The function is undefined for negative x to begin with... Stupid question.
     
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