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Differentiation of products

  1. Jan 1, 2005 #1
    [tex]x^2(x+1)(x-2)^7[/tex]
    Could someone show me how to start?
     
  2. jcsd
  3. Jan 1, 2005 #2
    Well you currently have a product of three functions. I suggest starting by 'combining' the first two parts of the product as follows.

    [tex]
    \frac{d}{{dx}}\left[ {x^2 \left( {x + 1} \right)\left( {x - 2} \right)^7 } \right] = \frac{d}{{dx}}\left[ {\left( {x^3 + x^2 } \right)\left( {x - 2} \right)^7 } \right]
    [/tex]

    Now just use the product rule to differentiate it.
     
  4. Jan 1, 2005 #3
    Ah!! I thought so to. But just wasn't sure. Thanks! Hapyy new year! :smile:
     
  5. Jan 1, 2005 #4

    dextercioby

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    In this simple case it works,as u're,mutiplying two simple polynomials.But what if thepolynomials had 50 terms?Would u do 2500 multiplications????
    Here's the deal:the Leibniz rule is very general.It can be easily extended to finite arbitrary number of factors:
    [tex](ABC...Z)'=A'BC...Z+AB'C...Z+ABC'...Z+...+ABC...Z' [/tex]
    In your case,there are only 3 very simple polynomials.If u want to,u may not make the multiplications after the differentiation.

    Daniel.

    EDIT:'Prime' denotes differentiation.
     
    Last edited: Jan 1, 2005
  6. Jan 1, 2005 #5
    Just checking, [tex]A'[/tex] is what I get after I differentiate A right?
     
    Last edited: Jan 1, 2005
  7. Jan 1, 2005 #6
    Yes it is.
     
  8. Jan 1, 2005 #7
    Thanks Nylex! Happy New Year!
     
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