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Logarithmic differentiation

  1. Dec 6, 2011 #1
    1. The problem statement, all variables and given/known data

    Use logarithmic differentiation to find dy/dx for y=(1+x)^(1/x).

    2. Relevant equations
    dy/dx


    3. The attempt at a solution
    ln y = ln (1+x)^(1/x)
    = (1/x) ln (1+x)
    (dy/dx) /y = (-1/x^2)(ln(1+x) + (1/x)(1/(1+x)

    dy/dx = y [(-1/x^2) ( ln(1+x) + x/(1+x) ]
    or (-1/x^2)( ln(1+x) + x/(1+x) ) (1+x)^(1/x)
     
  2. jcsd
  3. Dec 7, 2011 #2

    Mark44

    Staff: Mentor

    Do you have a question?
     
  4. Dec 7, 2011 #3
    Yes, I want to check my work if it's correct.
     
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