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Math Help - Derivative of This Function

  1. #1
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    Derivative of This Function

    20[(x/12) - ln(x/12)] +30

    ??

    I'm thinking...

    rearrange ln(x/12) to be
    ln (x) - ln (12)


    so derivative = 20[(1/12) - (1/x) - (1/12)]

    = -20/x

    ??
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  2. #2
    Super Member Gamma's Avatar
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    Quote Originally Posted by Equality View Post
    20[(x/12) - ln(x/12)] +30
    You are on the right track

    f(x)=20[(x/12) - ln(x/12)] +30 = \frac{20}{12}x -20ln(x) + 20 ln(12) + 30

    f'(x)=\frac{20}{12}-\frac{20}{x}


    All those terms without x's in them are just real numbers, so their derivative is 0, so there are really only two terms you have to worry about
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  3. #3
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    thanks for your reply.

    so it looks as though where i went wrong is calculating ln(12)

    i used 1/12 instead of (derivative of 12)/12 i.e. 0/12 i.e. 0
    Last edited by Equality; May 15th 2009 at 11:33 PM.
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  4. #4
    Super Member Gamma's Avatar
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    Yeah, I guess that is one way of thinking about it.

    Alternatively you know ln(12) is just a number you know? Like the derivative of 3 is 0. The derivative of \pi is 0. The derivative of \sqrt2 is 0. So The derivative of ln(12)=ln(2^23)=2ln(2)+ln(3) \approx 2(.69314) + 1.09861=2.48489 is just 0 as well.

    Sometimes these sorts of things can cause confusion, but for every c\in \mathbb{R}, we have \frac{d}{dx}c=0.
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  5. #5
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    got it!

    thanks heaps Gamma!
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