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Math Help - How would i rewrite this problem

  1. #1
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    How would i rewrite this problem

    Sorry im redoing it accidently submitted the wrong thing
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  2. #2
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    Here was my attempt it was actuly a derivative problem but i decided not to post in the calculus section.


    \frac {1}{3} (1-e^{6x})^{\frac{-2}{3}} * (- e^{6x} * 6)

    = (2 - 2e^{6x}) ^{\frac{-2}{3}} * -e^{6x}

     =  \frac{1}{(2-2e^{6x})^{\frac{2}{3}}} - e^{6x}
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  3. #3
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    Quote Originally Posted by x5pyd3rx View Post
    Here was my attempt it was actuly a derivative problem but i decided not to post in the calculus section.


    \frac {1}{3} (1-e^{6x})^{\frac{-2}{3}} * (- e^{6x} * 6)

    = (2 - 2e^{6x}) ^{\frac{-2}{3}} * -e^{6x}

     =  \frac{1}{(2-2e^{6x})}^{\frac{2}{3}}} - e^{6x}
    You can't distribute the two to the binomial expression because that expression is an infinite sum and the 2 is not raised to the same power.

    \frac{1}{3}(1-e^{6x})^{2/3} \cdot -6e^{6x}

    = 2e^{6x}(1-e^{6x})^{2/3}

    You cannot simplify that further.


    EDIT: If you're planning on finding the derivative use the product rule and the chain rule
    Last edited by e^(i*pi); February 20th 2010 at 11:14 AM. Reason: see post
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  4. #4
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    I'm assuming you are taking the derivative of f(x):

    f(x) = (1 - e^{6x})^{\frac{1}{3}}

    In that case, you made errors in both the second and third steps.

    (second step) You can't put the multiple of 2 inside the (1 - e^{6x})^{-\frac{2}{3}} term.

    (third step) You should be multiplying by -e^{6x}, not subtracting e^{6x}.
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  5. #5
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    Ahhh ok gotcha.. (no need to change the post btw)
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  6. #6
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    Quote Originally Posted by e^(i*pi) View Post
    \frac{1}{3}(1-e^{6x})^{2/3} \cdot -6e^{6x}

    = 2e^{6x}(1-e^{6x})^{2/3}
    A slight correction:

    \frac{1}{3}(1-e^{6x})^{-2/3} \cdot -6e^{6x}

    = -2e^{6x}(1-e^{6x})^{-2/3}
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  7. #7
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    Quote Originally Posted by icemanfan View Post
    I'm assuming you are taking the derivative of f(x):

    f(x) = (1 - e^{6x})^{\frac{1}{3}}

    In that case, you made errors in both the second and third steps.

    (second step) You can't put the multiple of 2 inside the (1 - e^{6x})^{-\frac{2}{3}} term.

    (third step) You should be multiplying by -e^{6x}, not subtracting e^{6x}.
    Your right... I did i just wrote it on here wrong. thanks for the help both of you
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  8. #8
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    So in that case i can rewrite it as


    <br /> <br />
= \frac{-2e^{6x}}{(1-e^{6x})^{2/3}}<br />
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  9. #9
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    Quote Originally Posted by x5pyd3rx View Post
    So in that case i can rewrite it as


    <br /> <br />
= \frac{-2e^{6x}}{(1-e^{6x})^{2/3}}<br />
    Correct.
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