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Math Help - Differentiation with quotient rule

  1. #1
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    Differentiation with quotient rule

    F(x)=\frac{x^4-5x^3+\sqrt{x}}{x^2}

    solution attempt: Book asks one to to try solving two ways once with quotient rule and once simplifying first. I have shown here only the quotient rule solution as that is giving me enough trouble to warrant a post

    With quotient rule,

     [(4x^3-15x^2+\frac{1}{2}x^\expfrac{-1/2})(x^2)] - [(2x)(x^4-5x^2+\sqrt{x})]

      = [4x^5-5x^4+\frac{1}{2} x^\expfrac{3/2}] - [2x^5-10x^4+2x(x)^\expfrac{1/2}]


    = \frac{2x^5+5x^4+\frac{1}{2}x^\expfrac{3/2}-2x(x)^\expfrac{1/2}}{x^4}

    this is where I am reluctant to continue as I'm unsure how to go about simplifying the exponents, in doing so I end up with:

     \frac{2x+5+\frac{1}{2}x-2x}{x^6}

    I could eliminate the  2x but I get the distinct feeling I performed an error 2 expressions ago... please show me my error
    Last edited by Foxlion; March 2nd 2011 at 05:52 PM.
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    Quote Originally Posted by Foxlion View Post
    F(x)=\frac{x^4-5x^2+\sqrt{x}}{x^2}

     [(4x^3-15x^2+\frac{1}{2}x^\expfrac{-1/2})(x^2)] - [(2x)(x^4-5x^2+\sqrt{x})]
    That -15x^2... What's the derivatvie of -5x^2?

    -Dan
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    typo in first expression, sorry
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Foxlion View Post

     [(4x^3-15x^2+\frac{1}{2}x^\expfrac{-1/2})(x^2)] - [(2x)(x^4-5x^2+\sqrt{x})]

      = [4x^5-5x^4+\frac{1}{2} x^\expfrac{3/2}] - [2x^5-10x^4+2x(x)^\expfrac{1/2}]
    Okay, let's look then at

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

    Look at the second term:
    (2x)(-5x^2) is equal to what?

    -Dan
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  5. #5
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    Quote Originally Posted by Foxlion View Post
    F(x)=\frac{x^4-5x^3+\sqrt{x}}{x^2}

    solution attempt: Book asks one to to try solving two ways once with quotient rule and once simplifying first. I have shown here only the quotient rule solution as that is giving me enough trouble to warrant a post

    With quotient rule,

     [(4x^3-15x^2+\frac{1}{2}x^\expfrac{-1/2})(x^2)] - [(2x)(x^4-5x^2+\sqrt{x})]

      = [4x^5-5x^4+\frac{1}{2} x^\expfrac{3/2}] - [2x^5-10x^4+2x(x)^\expfrac{1/2}]


    = \frac{2x^5+5x^4+\frac{1}{2}x^\expfrac{3/2}-2x(x)^\expfrac{1/2}}{x^4}

    this is where I am reluctant to continue as I'm unsure how to go about simplifying the exponents, in doing so I end up with:

     \frac{2x+5+\frac{1}{2}x-2x}{x^6}
    Surely that's not what was intended! \frac{x^4-5x^3+\sqrt{x}}{x^2}= \frac{x^4}{x^2}- \frac{5x^3}{x^2}+ \frac{x^{1/2}}{x^2}=  x^2- 5x+ x^{-3/2} is much simpler.

    I could eliminate the  2x but I get the distinct feeling I performed an error 2 expressions ago... please show me my error
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