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Thread: Differenciation Help needed.

  1. #1
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    Differenciation Help needed.

    i need to differenciate :

    $\displaystyle
    x^3(2x+6)^4
    $ using product rule


    i got to this stage :
    $\displaystyle x^3 \times 8(2x+6)^3 + (2x+6)^4 \times 3x^2 $

    but the answer stated in the textbook is $\displaystyle 2x^2(2x+6)^3(7x+9) $
    I think its the simplifying which i don't understand provided that the stage i got to is correct.
    any help is appreichated.

    Thank You
    Last edited by rpatel; Sep 20th 2007 at 12:31 PM.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    It is just rearranged.

    Factorise the expression that you got.

    --

    Careful... don't forget the chain rule.
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  3. #3
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    sorry i still don't understand do you mind please showing me exactly how it is done.

    thanks

    Kind Regards
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  4. #4
    Junior Member
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    $\displaystyle 8x^3(2x + 6)^3 + 3x^2(2x + 6)^4$

    Take out $\displaystyle x^2$...

    $\displaystyle x^2 ( 8x(2x + 6)^3 + 3(2x + 6)^4 )$

    Next, factor out $\displaystyle (2x + 6)^3$...

    $\displaystyle ( x^2 (2x + 6)^3 ) ( 8x + 3(2x + 6) )$

    $\displaystyle ( x^2 (2x + 6)^3 ) ( 8x + 6x + 18)$

    $\displaystyle ( x^2 (2x + 6)^3 ) ( 14x + 18 )$

    Grab a 2 out of there...

    $\displaystyle 2x^2 (2x + 6) (7x + 9)$

    -Scott
    Last edited by ScottO; Sep 20th 2007 at 03:29 PM. Reason: removed extra parens
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