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Math Help - Natural log derivatives? How?

  1. #1
    Newbie
    Joined
    Jan 2009
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    Question Natural log derivatives? How?

    This is the equation I have:

    Let f(x) = -4 \ln(5 x)
    Find  f'(x) =

    My Work Sheet says the answer is:
    <br />
-4/x<br />

    My question is, shouldn't it be somthing like:
    <br />
-20/5x<br />
    ...when you derive ln(5 x) shouldn't it become 1/5x and from there don't you have to use the chain rule on 5x and get 5?

    It seems to me you would only get  -4/x if f(x) = -4 \ln(x)

    What is it I don't understand?! Thank You
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  2. #2
    Junior Member
    Joined
    Sep 2008
    Posts
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    the thing with natural log derivatives is that (d/dx) ln(x) is actually (1/x)*x' (so 1 divided by the inside, then times the derivative of the inside)

    -4ln(5x) becomes -4*(1/5x)*5 = -4/x
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  3. #3
    Newbie
    Joined
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    Wow -20/5x = -4/x...

    Im dumb... haha I guess that's what doing hours upon hours of math does... just scrambles the brain.
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