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Math Help - derivatives of logarithmic functions

  1. #1
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    Question derivatives of logarithmic functions

    I got a different answer from the book, and I still right? what happened here?

    differentiate

    f(x)=log 2 (1-3x)

    Book answer: f'(x)=3/[(3x-1) ln 2]

    My answer: f'(x)=1/[(1-3x) ln 2]
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by thecount View Post
    I got a different answer from the book, and I still right? what happened here?

    differentiate

    f(x)=log 2 (1-3x)

    Book answer: f'(x)=3/[(3x-1) ln 2]

    My answer: f'(x)=1/[(1-3x) ln 2]

    You forgot to apply the chain rule!

    \frac{d}{\,dx}\log_2(1-3x)=\frac{1}{(1-3x)\ln 2}\cdot -3=\frac{-3}{(1-3x)\ln 2}=\color{red}\boxed{\frac{3}{(3x-1)\ln 2}}

    Does this make sense?

    --Chris
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  3. #3
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    yes, it does! i completely forgot!, thanks
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