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Logarithmic differentiation

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the derivative using logarithmic differentiation:
    y=(x+5)(x+9)

    3. The attempt at a solution

    lny=ln(x^2+14x+45)
    lny=(2x+14)/(x^2+14x+45)
    y'=(x^2+14x+45)((2x+14)/(x^2+14x+45))


    However, I know the derivative of the function is actually 2x+14. So I am wondering what is wrong with my process?

    UPDATE: Wow it only took typing my problem into this forum and making the post before I realized that I did do it right! You guys are good! lol sorry for wasting any ones time.
     
  2. jcsd
  3. Nov 10, 2012 #2

    Zondrina

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    Homework Helper

    Why wouldn't you just say :

    lny=ln((x+5)(x+9))
    ln y = ln(x+5) + ln(x+9)

    Now...

    y'/y = Take the derivative here

    Would've been muchhhh easier.
     
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