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Power rule

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data
    I promise this will be my last one :p

    For this function: [tex]f(x)=-4x^{3}+\frac{3}{x}+\sqrt{x}-2[/tex]
    What would be the derivative using the power rule?


    2. Relevant equations

    [tex]f(x)=-4x^{3}+\frac{3}{x}+\sqrt{x}-2[/tex]

    3. The attempt at a solution

    [tex]f'(x)=-12x^{2}-3x^{-2}-\frac{\sqrt{x}}{2}[/tex]

    However, this is wrong. Why?
     
  2. jcsd
  3. Sep 20, 2009 #2
    [tex]\sqrt{x} = x^\frac{1}{2}[/tex]

    Use the power rule and subtract one from that exponent.
     
  4. Sep 20, 2009 #3
    [tex]f'(x)=-12x^{2}-3x^{-2}+\frac{1}{2x^{1/2}}[/tex]

    1/2 - 1 = -1/2
     
  5. Sep 20, 2009 #4
    derivative of x^1/2 = 1/2 x^(-1/2)
     
  6. Sep 20, 2009 #5
    The exponent is -1/2, but that term should be positive.
     
  7. Sep 20, 2009 #6
    Could that be written as [tex]\frac{1}{2\sqrt{x}}[/tex]?
     
  8. Sep 20, 2009 #7
    [tex]f'(x)=-12x^{2}-3x^{-2}+\frac{1}{2x^{1/2}}[/tex]

    Like this?
     
  9. Sep 20, 2009 #8
    Yes, that's right. Didn't see your other post with the correct answer.
     
  10. Sep 20, 2009 #9
    I edited it :D
    I was just wondering because the book has a much different answer :/
     
  11. Sep 21, 2009 #10
    What does the book say?
     
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