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Derivative of y

  1. Apr 17, 2007 #1
    Hi there. Need a bit of help~

    y=sin^(2)x

    So the equation reads y equals sine squared times x

    Anyway, my teacher told me that in cases like these, you can move the exponent "outside," so that the equation can be written as y=(sinx)^2.

    So on to getting the derivative of the equation:

    I did the package rule, so y'=2(sinx)cosx

    Unfortunately, the answer on the worksheet I have is sin2x. No cosine. Am I not supoosed to do the package rule?? Or could it be simplified?? Or am I just doing something else wrong completely?

    Help~ TT__TT
     
  2. jcsd
  3. Apr 17, 2007 #2

    danago

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    Gold Member

    Have a look at the common trig identities :smile: Shouldnt be hard to see how they got to the next step.
     
    Last edited: Apr 17, 2007
  4. Apr 17, 2007 #3
    You're answer is right, but as danago said look at some trig identities, and it should seem very clear :P
     
  5. Apr 17, 2007 #4
    Heh... after staring at some trig identities that I've never saw before for about 20 minutes, I finally got it through my thick head what you guys were talking about... X/ Oh dear... Thanks a bunch!
     
  6. Apr 18, 2007 #5

    HallsofIvy

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    First of all [itex]sin^2(x)[/itex] does not read "y equals sine squared times x"! That's either very sloppy wording or you are completely misunderstanding. That notation means "First find sine of x. Then square hat." You are certainly not multiplying "sine" (which is a function not a value) by anything.
     
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