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Math Help - Natural logarithm question

  1. #1
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    Natural logarithm question

    Given the question 3(ln{sqrt(2x+3)})^2, find the derivative

    I used the formula for chain rule and then did the necessary algebra and got this:

    6(ln{sqrt(2x+3)})
    2x+3

    However the answer is listed as
    3ln(2x+3)
    2x+3

    Can someone tell me where I made my error?
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  2. #2
    Moo
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    Hello,

    There is no error

    The thing is :

    \log(a^n)=n \log(a)

    Plus \sqrt{b}=b^{\frac12}

    D'you see the trick ?
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  3. #3
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    So the upper term can simplify like this:

    6ln(2x+3)^1/2
    = 1/2(6ln(2x+3))
    =3ln(2x+3)

    ?
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  4. #4
    o_O
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    Exactly.
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