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1 more derivative problem

  1. Sep 30, 2007 #1
    1 more derivative problem!!

    1. The problem statement, all variables and given/known data
    Find the derivative of...
    2sinxcosx
    not simplified

    3. The attempt at a solution
    (2cosxcosx) - (2sinxsinx)

    I just want to make sure this is right
     
  2. jcsd
  3. Sep 30, 2007 #2

    rock.freak667

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    Homework Helper

    yes that is correct..but you should simplify cosxcosx to [tex]cos^2x[/tex] and likewise with the sinxsinx
     
  4. Sep 30, 2007 #3

    dynamicsolo

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    And, when you're done, does that result look like a trig identity you've seen before? Could you have gotten the same result by using a trig identity on 2 sin x cos x first?
     
  5. Feb 9, 2009 #4
    Re: 1 more derivative problem!!

    dy/dx = 2 sin x . -sin x +cos x . cos x= 2 ( cos squared - sin squared)

    So yes your correct
     
    Last edited: Feb 9, 2009
  6. Feb 9, 2009 #5

    HallsofIvy

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    Re: 1 more derivative problem!!

    Which, as dynamicsolo hinted, is the same as 2 cos(2x) and could have been done more simply by recognizing that 2 sin(x) cos(x)= sin(2x).
     
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