HELP! trouble factoring while using the chain rule + the product rule

Discussion in 'Community Discussion' started by macman2790, Feb 28, 2007.

  1. macman2790 macrumors 6502a

    macman2790

    Joined:
    Sep 4, 2006
    Location:
    Texas
    #1
    I'm having trouble factoring using the chain rule with the product rule. the answer is in the book but i cant figure out how to factor it out correctly. Will someone please walk me through the factoring part, i'm having trouble with every problem like this and i have very many. the problem is:
    differentiate:
    y = (1+4x)^5 (3+x-x^2)^8

    heres what I have so far:

    y'= [5(1+4x)^4(4)](3+x-x^2)^8 + [8(3+x-x^2)^7*(1-2x)(1+4x^5)

    now here's the answer:4(1+4x)^4(3+x-x^2)^7(17 + 9x - 21x^2)

    Thanks in advance for the help.
     
  2. swiftaw macrumors 603

    swiftaw

    Joined:
    Jan 31, 2005
    Location:
    Omaha, NE, USA
    #2
    y = (1+4x)^5 (3+x-x^2)^8

    y' = 20(1+4x)^4 (3+x+x^2)^8 + 8(1-2x)(3+x-x^2)^7 (1+4x)^5

    = 20(1+4x)^4 (3+x+x^2)^7 (3+x+x^2) + 8(1-2x)(3+x-x^2)^7 (1+4x)^4 (1+4x)

    = 4(1+4x)^4 (3+x+x^2)^7 [5 (3+x+x^2) + 2 (1-2x) (1+4x)]

    I think the answer follows from here by simplifying what is in [...]
     
  3. macman2790 thread starter macrumors 6502a

    macman2790

    Joined:
    Sep 4, 2006
    Location:
    Texas
    #3
    thank you very much, i should have a bit of an easier time simplifying the rest of the 15 product rule + chain rule problems:D
     
  4. macman2790 thread starter macrumors 6502a

    macman2790

    Joined:
    Sep 4, 2006
    Location:
    Texas
    #4
    = 20(1+4x)^4 (3+x+x^2)^7 (3+x+x^2) + 8(1-2x)(3+x-x^2)^7 (1+4x)^4 (1+4x)

    = 4(1+4x)^4 (3+x+x^2)^7 [5 (3+x+x^2) + 2 (1-2x) (1+4x)]

    does anyone mind telling me why 2(1+4x)^4 is simplifying to 4(1+4x), its just too late for me lol.:D
     
  5. swiftaw macrumors 603

    swiftaw

    Joined:
    Jan 31, 2005
    Location:
    Omaha, NE, USA
    #5
    ?

    Not sure where you are looking?

    I split the 20 up into 4*5, the 4 is still out front, the 5 is inside the [..]
     
  6. macman2790 thread starter macrumors 6502a

    macman2790

    Joined:
    Sep 4, 2006
    Location:
    Texas
    #6
    i just saw it right before you posted, thanks, like i said it's too late for math lol.
     
  7. swiftaw macrumors 603

    swiftaw

    Joined:
    Jan 31, 2005
    Location:
    Omaha, NE, USA
    #7
    It's never too late for math :D
     

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