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Math Help - [SOLVED] Quotient Differentiation

  1. #1
    Junior Member Evales's Avatar
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    [SOLVED] Quotient Differentiation

    Hey I have a question. I've had to differentiate something but the answer in the back of the book says otherwise.
    Which one is right? And If I'm wrong can you tell me how to do it?

    The first equation is the original f(x)
    The second is the answer from the book f '(x)
    The third is my answer.

    Thanks!
    Attached Thumbnails Attached Thumbnails [SOLVED] Quotient Differentiation-equ.bmp  
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by Evales View Post
    Hey I have a question. I've had to differentiate something but the answer in the back of the book says otherwise.
    Which one is right? And If I'm wrong can you tell me how to do it?

    The first equation is the original f(x)
    The second is the answer from the book f '(x)
    The third is my answer.

    Thanks!
    Yours should be \frac{1}{e^x+x}-\frac{(e^x+1)x}{(e^x+x)^2}

    It would have been better if you had provided your working, but it doesn't matter


    f(x)=\frac{x}{e^x+x}=\frac uv

    \begin{aligned} f'(x)&=\frac{u'v-uv'}{v^2} \\<br />
&=\frac{1 \cdot (e^x+x)-x(e^x+1)}{(e^x+x)^2} \ {\color{red}(1)} \\<br />
&=\frac{e^x+x}{(e^x+x)^2}-\frac{x(e^x+1)}{(e^x+x)^2} \\<br />
&=\frac{1}{e^x+x}-\frac{x(e^x+1)}{(e^x+x)^2} \end{aligned}


    From (1), we get :

    =\frac{e^x+x-xe^x-x}{(e^x+x)^2}=\frac{e^x-xe^x}{(e^x+x)^2}
    which is what your book gave.

    Is it better ?
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Evales View Post
    Hey I have a question. I've had to differentiate something but the answer in the back of the book says otherwise.
    Which one is right? And If I'm wrong can you tell me how to do it?

    The first equation is the original f(x)
    The second is the answer from the book f '(x)
    The third is my answer.

    Thanks!
    f(x) = \frac{x}{e^x + x}

    f'(x) = \frac{(1)(e^x + x) - (x)(e^x + 1)}{(e^x + x)^2}

    Which simplifies to the book's answer
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  4. #4
    Junior Member Evales's Avatar
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    Thanks so much!

    I see where I went wrong now.
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