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Math Help - Compostion of functions, Involving ln

  1. #1
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    Compostion of functions, Involving ln

    The question is:
    Differentiate: y=ln(8x^2+2)^4

    Now, the answers in the back give:
    32x/(4x^2+1)
    ----as the derivative. I had a problem with this Question/Answer combo... I would think that the derivative it gives would be for the function
    y=ln[(8x^2+2)^4]
    .... I believe there is a difference, and I would like to know if I am correct.
    Because I went about solving the question a different way, due to the way I see it written (I see it as y=[ln(8x^2+2)]^4 )
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  2. #2
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    Quote Originally Posted by mike_302 View Post
    The question is:
    Differentiate: y=ln(8x^2+2)^4

    Now, the answers in the back give:
    32x/(4x^2+1)
    ----as the derivative. I had a problem with this Question/Answer combo... I would think that the derivative it gives would be for the function
    y=ln[(8x^2+2)^4]
    .... I believe there is a difference, and I would like to know if I am correct.
    Because I went about solving the question a different way, due to the way I see it written (I see it as y=[ln(8x^2+2)]^4 )
    y = \ln(8x^2+2)^4 ... only the argument (8x^2+2) is raised to the 4th power

    y = [\ln(8x^2+2)]^4 ... the entire log is raised to the 4th power.


    y = \ln(8x^2+2)^4

    y = 4\ln(8x^2+2)<br />
    y' = 4 \cdot \frac{16x}{8x^2+2} = 4 \cdot \frac{8x}{4x^2+1} = \frac{32x}{4x^2+1}
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  3. #3
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    ahhhhhh, I forgot all about applying some log rules before doing the derivative. Good point!

    Thanks!
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