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Derivative of compound interest

  1. Nov 23, 2009 #1
    1. The problem statement, all variables and given/known data
    f(x) = (1/x+1)^x, find f'(x)


    2. Relevant equations
    derivative of a^x = ln(a) a^x


    3. The attempt at a solution
    When I differentiate i get ln((1+x)/x)*((1+x)/x)^x... However, this solution does not match what I should be getting. Am i differentiating wrong at some point? or are my notes that claim a^x = lna*a^x wrong...
     
  2. jcsd
  3. Nov 23, 2009 #2

    Dick

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    Your formula for a^x assumes a is a constant. The easiest way to handle this one is to use (1/x+1)=exp(ln(1/x+1)) so f(x)=exp((ln(1/x+1))*x). Now just differentiate and don't forget the chain rule.
     
  4. Nov 23, 2009 #3
    duh!!!!


    thanks so much dick I can't believe I stared at it for that long and didn't realize that.
     
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