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Math Help - Help finding derivative using definition (which results in a complex fraction)

  1. #1
    Newbie dannibambi's Avatar
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    Question Help finding derivative using definition (which results in a complex fraction)

    Hello! This is the last problem of the night (I promise!). Will someone please help me with the following problem; if I could use the quotient rule I wouldn't have had any problems, but here is the question:


    Find the derivative of
    Help finding derivative using definition (which results in a complex fraction)-mathway_-find-derivative-1.jpg
    using the definition of derivative.
    State the domain of the function and the domain of its derivative.



    When I worked it out, this was what I got:
    Help finding derivative using definition (which results in a complex fraction)-math-help.jpg

    But the answer I got using Mathway.com was:
    Help finding derivative using definition (which results in a complex fraction)-mathway-answer.jpg

    I could DEFINITELY use some help. Where did I go wrong?
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Help finding derivative using definition (which results in a complex fraction)

    so

     lim_{h \to 0} \frac{f(x+h) - f(x)}{h}  = \frac{\frac{3+x+h}{1-3x-3h} - \frac{3+x}{1-3x}}{h} = \frac{\frac{(3+x+h)(1-3x)-(3+x)(1-3x-3h)}{(1-3x-3h)(1-3x)}}{h}=  \frac{\frac{(3-3)+(x-x)+(9x-9x)+(3x^2-3x^2)+(9h+h)+(3xh-3xh)}{(1-3x-3h)(1-3x)}}{h}= \frac{10h}{h*(1-3x-3h)(1-3x)} = \frac{10}{(1-3x-3h)(1-3x)} =  \frac{10}{(1-3x)^2}
    Last edited by jakncoke; January 27th 2013 at 10:24 PM.
    Thanks from dannibambi
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  3. #3
    Newbie dannibambi's Avatar
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    Re: Help finding derivative using definition (which results in a complex fraction)

    I can't believe I made so many basic mistakes. Thank you so much for your help!! :-)
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