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Math Help - logarithmic differentiation

  1. #1
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    logarithmic differentiation

    why do we have to rewrite as  |y|=|x|^2|3x-1|^3 ?
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  2. #2
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    Re: logarithmic differentiation

    Because log function is not defined for negative numbers
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  3. #3
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    Re: logarithmic differentiation

    isnt it that ln|x|=\frac{1}{x} both lnx and ln(-x) equals to \frac{1}{x}, so it doesn't matter?
    and also, when it comes to rewriting using modulus, how do i know for sure the correct way to write it? why not |y|=|x^5(3x-1)^3|
    or |y|=|x|^5(3|x|-1)^3
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    Re: logarithmic differentiation

    logarithmic differentiation-26-may-13-2.png
    Thanks from muddywaters
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  5. #5
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    Re: logarithmic differentiation

    oh yeah thanks and sorry it should be  (ln|x|)'=\frac{1}{x}
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  6. #6
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    Re: logarithmic differentiation

    No, it should be (ln|x|)'= \frac{1}{|x|}.
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    Re: logarithmic differentiation

    Quote Originally Posted by HallsofIvy View Post
    No, it should be (ln|x|)'= \frac{1}{|x|}.
    why do you say so?
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  8. #8
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    Re: logarithmic differentiation

    i mean, is there some significance?? it seems the same to me in the end
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    Re: logarithmic differentiation

    Draw the graph of ln(x). It's derivative is always increasing so 1/x has to be positive for the domain of the original function. You can also draw the graph of 1/x. There is a positive and negative portion of the graph. The absolute value keeps only the positive portion. The first derivative tells you how the original function changes or how it's slope changes. As you get close to zero the slope gets really steep. Try putting really small positive numbers into 1/x. What happens?
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  10. #10
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    Re: logarithmic differentiation

    Quote Originally Posted by wondering View Post
    Draw the graph of ln(x). It's derivative is always increasing so 1/x has to be positive for the domain of the original function. You can also draw the graph of 1/x. There is a positive and negative portion of the graph. The absolute value keeps only the positive portion. The first derivative tells you how the original function changes or how it's slope changes. As you get close to zero the slope gets really steep. Try putting really small positive numbers into 1/x. What happens?
    ?? u get a huge number approaching infinity? but how is that related to what we're discussing?
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  11. #11
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    Re: logarithmic differentiation

    Quote Originally Posted by muddywaters View Post
    it should be  (\ln|x|)'=\frac{1}{x}
    That is correct. See here.
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  12. #12
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    Re: logarithmic differentiation

    You get a really small number approaching infinity and a really big number as you approach zero. Does that match how the slope of ln(x) changes from (0,inf)?
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