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Differentiation, Product Rule 3-terms

  1. Oct 27, 2009 #1
    1. The problem statement, all variables and given/known data

    f(x) = (2x-1)(3x-2)(5x+1) d/dx = ?

    Note that I am letting (2x-1)(3x-2) = f and 5x+1 = g

    2. Relevant equations

    d/dx (fg) = f d/dx g + g d/dx f

    3. The attempt at a solution

    d/dx y = (2x-1)(3x-2)d/dx(5x+1)+(5x+1)d/dx((2x-1)(3x-2))

    = (2x-1)(3x-2)(5)+ (5x+1)(2x-1)d/dx(3x-2)+(3x-2)d/dx(2x-1)
    = 5(2x-1)(3x-2) + 3(5x+1)(2x+1) + 2(3x-2)

    Can someone validate this answer for me?
     
  2. jcsd
  3. Oct 27, 2009 #2

    lanedance

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    Homework Helper

    missed a bracket here, should be
    = (2x-1)(3x-2)(5)+ (5x+1)[(2x-1)d/dx(3x-2)+(3x-2)d/dx(2x-1)]
    final answer looks good to me though, could always check by expanding it out

    now that you know it you can make the jump

    say
    y = fgh

    then
    y' = f'(gh) + f(gh)' = f'gh + fg'h + fgh'
     
    Last edited: Oct 27, 2009
  4. Oct 27, 2009 #3
    Thank you for the quick response.. much appreciated.
     
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