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Substitution Question

  1. May 26, 2010 #1
    Hey All,

    First post, hopefully it will be readable. I was going to try and word it correctly, but I might as well just post a problem I am having with a certain notation.

    Take integral of e^6x. Easy enough question. Using U substitution:

    u = 6x
    du/dx = 6
    du = 6 dx

    Integral above now equals 1/6 e^6x + C (so the 1/6 cancels with our 6 in 6 dx).

    Ok, now using dy/dx = dy/du * du/dx notation.

    e^6x let u = 6x
    y = e^u
    u = 6x

    dy/du = e^u
    du/dx = 6

    Since dy/dx = dy/du * du/dx, wouldn't the above equal e^6x * 6

    The second notation confuses me a bit... Any help to explain would be appreciat
    Thanks,

    M
     
    Last edited by a moderator: May 27, 2010
  2. jcsd
  3. May 26, 2010 #2
    dy/dx=6e^6x is correct,
    if y=e^6x

    You've differentiated y wrt x. It's correct, just not what you wanted to find.
     
  4. May 27, 2010 #3

    HallsofIvy

    User Avatar
    Science Advisor

    Yes, it would. One is integrating, the other differentiating. Since those are "opposite" operations, it shouldn't surprise you that one involves dividing by 6 and the other involves multiplying by 6.

     
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