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Find the derivative of the function

  1. Jul 15, 2012 #1
    1. Find the derivative of the function using the quotient rule and also by simplifying



    2. F(x) = (x - 3x√x)/√x



    3. (9x^2 - x - 8) / (2x √x)
     
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  3. Jul 15, 2012 #2

    eumyang

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    You need to show us your attempt at working these out before we can help you.
     
  4. Jul 15, 2012 #3
    [itex]\sqrt{x}[/itex] (1-3(1[itex]/[/itex]2[itex]\sqrt{x}[/itex])) - (x-3x[itex]\sqrt{x}[/itex])(1[itex]/[/itex]2[itex]\sqrt{x}[/itex])[itex]/[/itex][itex]\sqrt{x}[/itex][itex]^{2}[/itex] = (1-9-x+9x[itex]^{2}[/itex])[itex]/[/itex](2[itex]\sqrt{x}[/itex][itex]\sqrt{x}[/itex][itex]^{2}[/itex]) = (9x[itex]^{2}[/itex]-x-8) [itex]/[/itex] (2x[itex]\sqrt{x}[/itex])
     
  5. Jul 15, 2012 #4

    Mentallic

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    [tex]\frac{d}{dx}x^n=nx^{n-1}[/tex]
    And so for the numerator you should have,
    [tex]\frac{d}{dx}\left(x-3x\sqrt{x}\right)[/tex]
    [tex]=\frac{d}{dx}\left(x-3x^{3/2}\right)[/tex]
    [tex]=1-3\left(\frac{3}{2}\cdot x^{1/2}\right)[/tex]
     
  6. Jul 15, 2012 #5

    HallsofIvy

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    Personally, I wouldn't have used the quotient rule for this at all. I would have written the function as [itex]F(x)= (x+ x^{3/2})x^{-1/2}= x^{1/2}+ x[/itex]

    The other function is [itex](9x^2- x- 8)(1/2)(x^{-3/2}= (1/2)(9x^{1/2}- x^{-1/2}- 9x^{-3/2})[/itex]
     
  7. Jul 15, 2012 #6
    It said to use both simplification and the quotient rule and to show that the two are the same.
     
  8. Jul 15, 2012 #7
    It said to use both simplification and the quotient rule and to show that the answers are the same.
     
  9. Jul 15, 2012 #8
    Here's what I got for the quotient rule: [itex]\frac{1}{2}[/itex](x[itex]^{-1}[/itex] - x[itex]^{-1/2}[/itex])
     
  10. Jul 15, 2012 #9
    For simplification, I get: (x-3x[itex]^{3/2}[/itex]) x[itex]^{-1/2}[/itex] = (x-[itex]\frac{9}{2}[/itex]x[itex]^{1/2}[/itex]) x[itex]^{-1/2}[/itex]
     
  11. Jul 16, 2012 #10

    micromass

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    Please show us the actual steps you went through. What did you do to obtain those results?
     
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