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Is this derivative correct?

  1. Mar 14, 2007 #1
    1. The problem statement, all variables and given/known data

    Find derivative of function: [tex]f\left(x\right)=\frac{1}{1+e^{x}}[/tex]

    2. Relevant equations

    quotient rule.

    3. The attempt at a solution

    hopefully this is the solution:
    [tex]f^{'}\left(x\right)=\frac{e^{x}}{(1+e^{x})^{2}}[/tex]
     
    Last edited: Mar 14, 2007
  2. jcsd
  3. Mar 14, 2007 #2
    Really close, but not exactly. Are you sure about the denominator? How is it different from that of the original function?
     
  4. Mar 14, 2007 #3
    oh, thanks! i had that messed up on my paper too.
     
  5. Mar 14, 2007 #4

    dextercioby

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    The derivative is okay up to the overall "-" sign which should be absent in the numerator.
     
  6. Mar 14, 2007 #5
    i think its fixed now...
     
  7. Mar 14, 2007 #6

    dextercioby

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    Still incorrect. Remember that

    [tex] \frac{d}{dx}\left(\frac{1}{f(x)}\right)=-\frac{f'(x)}{f^{2}(x)} [/tex]
     
  8. Mar 14, 2007 #7
    oh, i know this should be easy but i've been studying calculus for only 48 hours, so i appreciate the patience and help.

    I could easily rewrite the equation like this [tex](1+e^{x})^{-1}[/tex] and derivate it, but i should know how to do it the other way.
     
    Last edited: Mar 14, 2007
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