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Basic derivative question

  1. Oct 22, 2007 #1
    [SOLVED] basic derivative question

    since d/dx(e^x) = e^x

    does d/dx(e^[-x]) = e^[-x]

    and d/dx(e^[x+1])= e^(x+1)

    the answer to one of my homework problems is different from my friends and I think that it is because I am mistaken about the stuff I just posted
     
  2. jcsd
  3. Oct 22, 2007 #2

    cristo

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    No; [itex]\frac{d}{dx}(e^{f(x)})=f'(x)e^{f(x)}[/itex]. Since in your first case, f(x)=1. f'(x)=1 so it doesn't matter, but it does for the second.
     
  4. Oct 22, 2007 #3
    hmmm, what is wrong with this:

    d/dx(e^(x+1)) = d/dx(e^[x] * e^[1]) = e^[x] * d/dx(e) + e * d/dx(e^x) = e^x * (0) + e * e^[x]= e^(x+1)
     
  5. Oct 22, 2007 #4

    cristo

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    Nothing; that's correct. Alternatively, using the notation in my previous post, we have that f(x)=x+1, and so f'(x)=1 => d/dx(e^{x+1})=e^{x+1}
     
  6. Oct 22, 2007 #5
    I thought you said that the second one isn't true?
     
  7. Oct 22, 2007 #6
    I am confused; is d/dx(e^(x+1)) = e^(x+1)
     
  8. Oct 22, 2007 #7

    cristo

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    I did; the second one being d/dx(e^{-x}).
     
  9. Oct 22, 2007 #8
    how can I find the derivative of e^[-x]

    sorry for the confusion
     
  10. Oct 22, 2007 #9
    wait, I did this to it... does this work:

    e^-x = 1/e^x = e^x(0) + (1)(e^x)
     
  11. Oct 22, 2007 #10
    I read post #2, I'm not familiar with that notation... I have never seen it before.
     
  12. Oct 22, 2007 #11

    cristo

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    No, you need to use the quotient rule to differentiate quotients, something you may not have done yet.

    Instead, read post #2. What is f(x) in this case?
     
  13. Oct 22, 2007 #12
    f(x) = -x

    right?
     
  14. Oct 22, 2007 #13

    cristo

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    Correct. So, what's f'(x)? Note that the prime here just means "derivative wrt x" so, f'(x)=d/dx(f(x))=d/dx(-x)

    [NB: I deleted my post a few above, the one you quoted, as it seemed a little abrupt. Sorry about that.]
     
  15. Oct 22, 2007 #14
    which is -1?
     
  16. Oct 22, 2007 #15

    cristo

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    Yup, and so, using the formula in #2, what is the derivative of e^{-x}?
     
  17. Oct 22, 2007 #16
    -e^{-x} ?
     
  18. Oct 22, 2007 #17

    cristo

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    Correct!
     
  19. Oct 22, 2007 #18
    ugh, Im screwing up somewhere here...

    e^{-x} = 1/(e^x) if I apply the quotient rule... [e^x * (0) - (1) * e^x] / (e^x)^2

    -(e^x)/(e^{2x})

    EDIT: switched signs
     
    Last edited: Oct 22, 2007
  20. Oct 22, 2007 #19
    nm, after I cancel I get the same thing...

    thank you very much for your help
     
  21. Oct 22, 2007 #20
    would you mind taking a look at the problem that started all of this madness?
     
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