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Math Help - Logarithmic functions help.

  1. #1
    RedBarron
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    Logarithmic functions help.

    Im taking Business calc so it's not nearly as hard as normal calc, and I have a few questions on a take home quiz I have. If any one could help me it would be greatly appreciated.

    Find the derivative, do not need to simplify

    g(x)=ln(2x-3/x^2-4)

    and f(x)=(ln(12x^2+5))^25

    lastly y=e^x ln(5x)

    Thanks a lot, im pretty much done with the quiz im just not sure on these 3 probs
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  2. #2
    o_O
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    Some of the questions are a bit ambiguous but seems like they involve the application of the chain rule which says:
    \left[f(g(x))\right]' = f'\left(g(x)\right) \cdot g'(x)

    For: y = ln\left(\frac{2x-3}{x^{2}-4}\right)
    Let: f(x) = ln(x) \quad \quad g(x) = \frac{2x - 3}{x^{2}-4}

    Applying the formula:
    \left[ ln\left(\frac{2x-3}{x^{2}-4}\right) \right]' = \underbrace{\frac{1}{g(x)}}_{(\ln x)' = \frac{1}{x}} \cdot \: \:g'(x)
     = \frac{1}{\frac{2x - 3}{x^{2}-4}} \cdot \left(\frac{2x-3}{x^{2}-4}\right)'
    = \frac{x^{2} - 4}{2x - 3} \cdot \underbrace{\left(\frac{2x-3}{x^{2}-4}\right)'}_{\mbox{Quotient Rule}}

    See if you can apply the chain rule to the other questions.
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