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Factored form of a derivative

  1. Nov 18, 2011 #1
    1. The problem statement, all variables and given/known data
    use product rule to find the derivative of g(x)=(2x+1)^2(x-7)^3


    2. Relevant equations
    i've applied chain rule and product rule to get...


    3. The attempt at a solution
    4(2x+1)(x-7)^3+3(2x+1)^2(x-7)^2

    i need to factor out to get the following..
    5(x-7)^2(2x-5)(2x+1)
    That's the final answer from the book. But the steps to get there... I'm lost. Can anyone help me out on getting it to the factored form?
     
  2. jcsd
  3. Nov 18, 2011 #2

    Mark44

    Staff: Mentor

    Look for factors that are common to both terms.
    4(2x+1)(x-7)3+3(2x+1)2(x-7)^2
    = (2x+1)(x - 7)2[4(x - 7) + 3(2x + 1)]

    Now combine the terms in the brackets and pull out the common factor there, and you'll have what you need.
     
  4. Nov 18, 2011 #3
    thank you kind sir, you have saved me many hours of frustration!
     
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