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Differentiating natural logs and exponential functions?

  1. Apr 13, 2009 #1
    Hey all, I'm really having a hard time figuring out a couple of problems in which I have to differentiate:

    1: [tex] \frac{e^3^x}{\ln x} [/tex]

    I just don't know how to put it together... I know that [tex]e^3^x[/tex] is [tex]3e^3^x[/tex], and I know that you can't different [tex]\ln x[/tex], so I dunno what to do from there...

    And:

    2: [tex] \ln(e^-^2^x + e^-^x)[/tex]

    Totally not sure what to do there... Any help would be appreciated, I've looked online for similar examples and couldn't really find anything relevant to help me. Thanks!
     
  2. jcsd
  3. Apr 13, 2009 #2

    Hootenanny

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    Let's take the first question first,
    Correct.
    Erm... yes you can!

    HINT: Let y = lnx, then x = ey. Now differentiate x = ey with respect to x.
     
  4. Apr 13, 2009 #3
    Hrm, I'm feeling a bit retarded so bear with me, hehe. So, [tex]\frac {1}{x}[/tex]?
     
  5. Apr 13, 2009 #4

    Hootenanny

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    Correct :biggrin:

    So as far as putting it all together, can you suggest anything? Perhaps some sort of rule...?
     
  6. Apr 13, 2009 #5
    I'm really retarded at math, ugh... Hehe. So I have [tex]\frac {3e^3^x}{1/x}[/tex] ... Pretty sure I'm lost on what to do from there. :(
     
  7. Apr 13, 2009 #6

    Hootenanny

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    No that is not correct.

    [tex]\frac{d}{dx} \frac{f\left(x\right)}{g\left(x\right)} \neq \frac{f^\prime\left(x\right)}{g^\prime\left(x\right)}[/tex]

    What 'rules' of differentiation do you know?
     
  8. Apr 13, 2009 #7
    Not sure of any rules by name... I'm going to have to research more examples, I'm so rusty in math that I am unsure...
     
  9. Apr 14, 2009 #8

    Hootenanny

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    Try searching for the quotient rule, or the product rule and chain rule.
     
  10. Apr 14, 2009 #9
    I kinda give up on the first one, heh... Can someone tell me if I have #2 right?:

    Answer: [tex]\frac {1 - e^-^2^x}{e^-^x + e^-^2^x} [/tex]
     
  11. Apr 14, 2009 #10

    Pengwuino

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    The quotient rule and product rule explains how to differentiate two functions that divide are divided by or multiplied by eachother. Just look that up and identify f(x) and g(x) (that is the standard notation at least).

    For #2, it isn't correct. What did you do to come up with that answer?
     
  12. Apr 14, 2009 #11
    Mirth, can you show us step by step how you differentiated that expression?
     
  13. Apr 15, 2009 #12

    tiny-tim

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    Hi Mirth! :smile:
    ok, do you recognise this one by face :wink:

    (fg)' = … ? :smile:
     
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