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Math Help - Differentiate the function -

  1. #1
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    Differentiate the function -

    y = ln(4x/5-3x)

    What I have done is -

    ln4x - ln(5-3x)

    = dy/dx = 1/4x - 1/(5-3x)

    = (5-3x-4x)/4x(5-3x)

    Which is the wrong answer, please help?
    I hope I have posted this in the right place, my apologies if not?
    Last edited by HelenC; July 20th 2011 at 12:24 PM. Reason: bad layout and typing
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Differentiate the function -

    U have to use the chain rule, because you're dealing with composite functions:
    You're first step is good. But then it went wrong, because you didn't use the chain rule:
    If you want to calculate for example:
    D[\ln(5-3x)]
    Let 5-3x=u
    so you get:
    D[\ln(u)]=\frac{Du}{u}=\frac{D(5-3x)}{5-3x}= \frac{-3}{5-3x}

    Use also the chainrule to calculate D[\ln(4x)] or notice that
    \ln(4x)=\ln(4)+\ln(x)
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