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How to differentiate e^|x|

  1. Sep 5, 2008 #1
    1. The problem statement, all variables and given/known data
    a)How to differentiate fx=e^|x|?
    b)Why when x = 0, f'(x) is undefined

    2. Relevant equations



    3. The attempt at a solution
    Is it d/dx e^|x| = e^|x|? I have no idea for this question.
     
    Last edited: Sep 5, 2008
  2. jcsd
  3. Sep 5, 2008 #2

    Dick

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    Re: Differentiation

    |x|=x if x>=0 and |x|=(-x) if x<0. Split the problem into those two cases. To find out what happens AT x=0 look at the limits from both sides.
     
  4. Sep 5, 2008 #3
    Re: Differentiation

    So there are two answer right? -1/e^x and e^x. Why f'x is undefined at x = 0?
     
  5. Sep 5, 2008 #4
    Re: Differentiation

    Hello, please i still don't get it. I sketch 2 graph from the equation and at x = 0, there is a line there. But why f'(x) for e^|x| is undefined when x = 0?
     
  6. Sep 5, 2008 #5

    tiny-tim

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    Hi takercena! :smile:

    Your sketch shows two graphs, reflections of each other, joined together …

    do they join smoothly, or with a corner? :wink:
     
  7. Sep 5, 2008 #6

    Dick

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    Re: Differentiation

    There aren't really two answers, it just that the formula for the answer looks different for x>0 than it does for x<0. If x is close to 0 and negative f'(x)~(-1), if positive then f'(x)~1. There's a sharp corner on the graph of f(x) at x=0, just like on |x|. So f(x) doesn't have a well defined slope there.
     
  8. Sep 5, 2008 #7
    Re: Differentiation

    Oh i see. Thanks
     
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