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Differentiating logarithmic functions

  1. May 1, 2010 #1
    1. The problem statement, all variables and given/known data

    Differentiate the following:

    y = e4x/x2+1


    2. The attempt at a solution

    I know you have to use quotient rule here.

    so I wrote out (x2+1)* d/dx e4x) - d/dx (x2+1)* e4x all over (x2 + 1) 2

    I have no idea how to continue on from here...how would you differentiate e to the power of 4x without this technique: I let u = 4x, then
    y = e^u
    dy/du = e^u = e^(4x)
    du/dx = 4

    dy/dx = (dy/du)(du/dx) = 4e^(4x)

    If someone could please provide a full solution, this is really appreciated, I've got a test coming up very very soon!
     
  2. jcsd
  3. May 1, 2010 #2
    So far, so good. The derivative of e^(4x) = 4e^(4x).
     
  4. May 1, 2010 #3
    Ok I finished the entire problem and got the right answer, thanks for the confirmation that my derivative was right!
     
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