Differentiating natural logs and exponential functions?

  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. Hootenanny

    Hootenanny 9,679
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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. Hrm, I'm feeling a bit retarded so bear with me, hehe. So, [tex]\frac {1}{x}[/tex]?
     
  5. Hootenanny

    Hootenanny 9,679
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    Correct :biggrin:

    So as far as putting it all together, can you suggest anything? Perhaps some sort of rule...?
     
  6. 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. Hootenanny

    Hootenanny 9,679
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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. 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. Hootenanny

    Hootenanny 9,679
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    Try searching for the quotient rule, or the product rule and chain rule.
     
  10. 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. Pengwuino

    Pengwuino 7,118
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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. Mirth, can you show us step by step how you differentiated that expression?
     
  13. tiny-tim

    tiny-tim 26,053
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    Hi Mirth! :smile:
    ok, do you recognise this one by face :wink:

    (fg)' = … ? :smile:
     
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