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Homework Help: Find the double derivate of

  1. Dec 19, 2012 #1
    1. The problem statement, all variables and given/known data

    f(x) = (-5x^2+3x) / (2x^2-5)

    2. Relevant equations

    f 'x)=
    (-6x^2+50x-15) / ( 2x^2-5)^2

    3. The attempt at a solution
    f ''x= ?
  2. jcsd
  3. Dec 19, 2012 #2


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    Staff: Mentor

    Can you please show all the steps you used to take the first derivative?
  4. Dec 19, 2012 #3
    f'(x) = (2x^2 -5)((-10x+3) -(-5x^2+3x)4x) / 2x^2-5
    = -20x^3 +6x^2+50x-15+20x^3-12x^2 / (2x^ - 5)^2
    = -6x^2 +50x-15 / (2x^2 - 5)^2
  5. Dec 19, 2012 #4


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    Staff: Mentor

    Thanks, that makes it much easier to check. I think it's correct so far, now just apply the quotient rule one more time to get the second derivative...
  6. Dec 19, 2012 #5


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    Homework Helper

    Either use the quotient rule on your first derivative (which is right), or use the second derivative quotient rule, or use the product rule.

    [tex]\left( \dfrac{u}{v} \right) ^{\prime \prime}=\dfrac{u^{\prime \prime} v^2-2u^\prime v v^\prime+2u (v^\prime)^2-u v^{\prime \prime}}{v^3}[/tex]
  7. Dec 19, 2012 #6


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    Staff Emeritus
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    Homework Helper
    Gold Member

    It helps to use sufficient number of parentheses. A little spacing can also help.
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