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Homework Help: Need formula or how to

  1. Nov 4, 2007 #1
    [SOLVED] need formula or how to...

    y= ln ex/ex (x is the power)
     
  2. jcsd
  3. Nov 4, 2007 #2

    rock.freak667

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    uhm use the "^" to represent powers, for example, x squared is written as x^2

    and please state your question better
     
  4. Nov 4, 2007 #3
    Differentiate:

    y= ln e^x/e^x


    Thanks!
     
  5. Nov 4, 2007 #4

    rock.freak667

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    So the question is to differentiate

    [tex] y=\frac{ln e^x}{e^x}[/tex] ?


    if it is...what rule do you think you would use when you need to differentiate something of the form [itex]y=\frac{u}{v}[/itex] ?
     
  6. Nov 4, 2007 #5
    quotient rule.
    which is: first, derivative of second, minus second, derivative of first, divided by first squared. (but, i'm still stuck. could you work it out for me?)
     
    Last edited: Nov 4, 2007
  7. Nov 4, 2007 #6

    rock.freak667

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    Well firstly...lne^x can be simplified to xlne which is just x

    so you really want to find [tex]\frac{d}{dx}(\frac{x}{e^x})[/tex]

    so if u= x => [itex]\frac{du}{dx}=1[/itex]
    and v=e^x => [itex]\frac{dv}{dx}=e^x[/itex]

    the formula is
    [tex] \frac{d}{dx}(\frac{u}{v}) =\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}[/tex]


    so then you'll have
    [tex]\frac{d}{dx}(\frac{x}{e^x}) = \frac{(e^x)(1) -(x)(e^x)}{(e^x)^2}[/tex]

    then you will simplify it
     
  8. Nov 5, 2007 #7
    thanks a lot. you made it very easy to understand. only part i didn't get is it says answer should be 1-x/e^x. what cancels out the power in the denominator?


    Thanks again!
     
  9. Nov 5, 2007 #8

    rock.freak667

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    ...well the e^x in the numerator can be factored out and it will cancel with an e^x in the denominator...so giving you your answer
     
  10. Nov 5, 2007 #9
    oh, i see. thank you very much.. :)
     
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