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Derivative of (x^2+5x-1)/(x^2)

  1. Jun 15, 2010 #1
    1. The problem statement, all variables and given/known data Find the first derivative of [...] (below)



    2. Relevant equations

    ((x^2)+5x-1)/(x^2)

    3. The attempt at a solution

    (x^2+5x-1)/(x^2)

    [tex]y' = \frac{(x^2)(2x+5-0)-((x^2)+5x+-1)(2x)}{x^4}

    \\
    y' = \frac{2x^3+5x^2-2x^3-10x^2+2x}{x^4}

    \\ y' = \frac{(-5x^2)+2x}{x^4}

    \\ y' = \frac{-5x+2}{x^3}

    [/tex]

    Is this correct? It feels "off."
     
    Last edited: Jun 15, 2010
  2. jcsd
  3. Jun 15, 2010 #2
    thats what i got.... =]
     
  4. Jun 15, 2010 #3
    Cool. Thank you. :)
     
  5. Jun 15, 2010 #4

    HallsofIvy

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    However, the simplest way to do that is write
    [tex]\frac{x^2+ 5x- 1}{x^2}= \frac{x^2}{x^2}+ \frac{5x}{x^2}- \frac{1}{x^2}= 1+ 5x^{-1}- x^{-2}[/tex]

    The derivative of that is, of course, [itex]-5x^{-2}+ 2x^{-3}[/itex].

    Can you see that that is equal to your result?
     
  6. Jun 15, 2010 #5
    You can also apply the product rule if HallsofIvy's method doesn't work out (for example, if the denominator is more complicated).
     
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