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Are these equal?

  1. Aug 8, 2011 #1
    According to Wolfram|Alpha, sometimes, the derivative of arctangent is

    [tex]\frac{d}{dx}\arctan x =\frac{1}{1+{x}^{2}}[/tex]

    and sometimes,

    [tex]\frac{d}{dx}\arctan x =\frac{\arctan x}{x}[/tex]

    So are both of them equal?

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  3. Aug 8, 2011 #2
    The second case is actually
    [tex]\frac{d}{d\times x}\arctan (x)=\frac{\arctan (x)}{x}[/tex].
  4. Aug 8, 2011 #3


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    Okay, you have lost me. What does
    [tex]\frac{d}{d\times x}[/tex]
  5. Aug 8, 2011 #4
    d over d multiplied by x, where d is a constant. Wolframalpha simplifies this to 1/x.
  6. Aug 9, 2011 #5
    Oh. So that must have happened the other time too...
  7. Aug 9, 2011 #6
    Notice the blank between d and x in the left one.
    What input did you give in each time?

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  8. Aug 9, 2011 #7


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