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Math Help - derivative of a rational function

  1. #1
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    Differentiating a Rational Function

    Look at the image attached: It shows the differentiation of a rational function using
    Wolfram Alpha.
    I am having difficulties understanding why the final calculation of the derivative is equal to:
    -\frac{\7}{\ 2(x-2)^2}

    *Note: The final solution is not shown on the image attached.
    The entire thing can be viewed here:

    http://www.wolframalpha.com/input/?i=Derivative+Calculator&f1=%28x%2B5%29%282x-4%29^-1&f=Derivative.derivativefunction_%28x%2B5%29%28 2x-4%29^-1&a=*FVarOpt-_**Derivative.derivativevariable--

    Looking at the steps in the image attached, I understand everything that's happening up until the final line.

    From my interpretation it seems it should be:

    \frac {\1(2x-4)-2(x+5)(1)}{\2(x-2)^2}

    = \frac {2x-4-2x-10}{\(2x-4)^2}

    which:

    = -\frac {\14}{\(2x-4)^2}

    Where is the -7 coming from? What steps am I missing and what am I doing wrong?
    Attached Thumbnails Attached Thumbnails derivative of a rational function-rf_d.gif  
    Last edited by raymac62; September 11th 2011 at 05:21 PM.
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Differentiating a Rational Function

    It's algebra.
    (2x - 4)^2 = [2(x - 2)]^2 = 4(x - 2)^2
    The 4 reduces with the 14.
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  3. #3
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    Re: Differentiating a Rational Function

    Quote Originally Posted by TheChaz View Post
    It's algebra.
    (2x - 4)^2 = [2(x - 2)]^2 = 4(x - 2)^2
    The 4 reduces with the 14.
    I see! So simple. By factoring out the two it's simply diving the expression by two. Hence, we divide the numerator by 2 and it equals 7. Thank you so much.

    You pointed out exactly what I needed to see. It's funny because I wasn't paying attention to the fact that the expression was modified.
    2(x-2)^2

    I was immediately interpreting that as (2x-4)^2 which is incorrect. Exponents first!
    You knew how I was seeing it the wrong way. Very good insight.
    Last edited by raymac62; September 11th 2011 at 05:53 PM.
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