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Math Help - Y=X^(2)e^(cos2x) Find Y'

  1. #1
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    Thumbs down Y=X^(2)e^(cos2x) Find Y'

    Find Y' when Y= X^(2)e^(cos2x)

    Y= X^2e^{cos2x}

    These are the steps my teacher wrote down on the board. She used the Product rule.

    a) Y'= [{X^(2)}' *{e^(cos2x)}] + [{X^(2)} *{e^(cos2x)}']

    b) Y' = 2Xe^(cos2x) + X^(2)e^(cos2x) * [1-2sin(2x)]

    c) Y' = 2Xe^(cos2x)[1-2sin(2x)]

    So my questions are.
    1) Where did that 1 come from?
    2) How to go from step b to step c. Especifically why did X^(2)e^(cos2x) disapear in the final answer.
    Last edited by Brazuca; August 22nd 2009 at 05:35 PM.
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  2. #2
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    Quote Originally Posted by Brazuca View Post
    Find Y' when Y= X^(2)e^(cos2x)

    Y= X^2e^{cos2x}

    These are the steps my teacher wrote down on the board. She used the Product rule.

    a) Y'= [{X^(2)}' *{e^(cos2x)}] + [{X^(2)} *{e^(cos2x)}']

    b) Y' = 2Xe^(cos2x) + X^(2)e^(cos2x) * [1-2sin(2x)]

    c) Y' = 2Xe^(cos2x)[1-2sin(2x)]

    So my questions are.
    1) Where did that 1 come from?
    2) How to go from step b to step c. Especifically why did X^(2)e^(cos2x) disapear in the final answer.
    correction ...

    x^2e^{\cos(2x)}

    2xe^{\cos(2x)} + x^2e^{\cos(2x)} [-2\sin(2x)]

    factor out 2xe^{\cos(2x)} from both terms ...

    2xe^{\cos(2x)}[1 - x\sin(2x)]
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  3. #3
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    Unhappy

    Wait then did my teacher do this one wrong?

    Also I don't understand how you factored out <br />
2xe^{\cos(2x)}<br />
from both terms.
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  4. #4
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    Quote Originally Posted by Brazuca View Post
    Wait then did my teacher do this one wrong?

    can't say ... I wasn't there. did you copy it correctly?

    Also I don't understand how you factored out <br />
2xe^{\cos(2x)}<br />
from both terms.
    2xe^{\cos(2x)} + x^2 e^{\cos(2x)}[-2\sin(2x)] =

    \textcolor{red}{2xe^{\cos(2x)}} - \textcolor{red}{2x e^{\cos(2x)}}[x\sin(2x)]

    factor out \textcolor{red}{2xe^{\cos(2x)}} ...

    \textcolor{red}{2xe^{\cos(2x)}}[1 - x\sin(2x)]
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  5. #5
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    Oh I understand it now. I just had to seperate the Xs from the Es in order for it all to click.
    Last edited by Brazuca; August 22nd 2009 at 08:44 PM.
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