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Taking the derivative

  1. Sep 3, 2009 #1
    1. The problem statement, all variables and given/known data
    taking the derivative of this:(2x+1)^3(3-x)^2

    Answer Choices
    a.) 2(2x+1)^2(3-x)(x-10)
    b.) -2(2x+1)^2(3-x)(x-10)
    c.) 2(2x+1)^2(3-x)(5x-3)
    d.) -2(2x+1)^2(3-x)(5x-8)
    e.) -12(2x+1)^2(3-x)



    2. Relevant equations
    Product rule and chain rule


    3. The attempt at a solution
    i was thinking of using product rule and then the chain rule

    after i used the product and chain rule i get 2(3)(2x+1)^2(3-x)^2+(-1)(3-x)(2x+1)^3 ..but then when i look at the answer choices it doesnt match any am i missing a step or..?
     
    Last edited: Sep 3, 2009
  2. jcsd
  3. Sep 3, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    hey ilent saber, i'd check your working, i tink you missed a factor of 2 in the 2nd half of product rule

    then look at grouping terms with (2x+1)^2(3-x), then simplifying the rest
     
  4. Sep 4, 2009 #3
    Do it this way:

    [tex](2x+1)^3(3-x)^2[/tex]

    [tex]u=2x+1, z=3-x[/tex]

    [tex][(2x+1)^3(3-x)^2]'=[((2x+1)^3)'(3-x)^2+(2x+1)^3((3-x)^2)']=[(u^3)'u'(3-x)^2+(2x+1)^3((z^2)'z')][/tex]

    Now just find the derivatives of the remaining terms. :smile:
     
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