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Math Help - [SOLVED] Derivatives of cos and sin (again)

  1. #1
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    Question [SOLVED] Derivatives of cos and sin (again)

    okay so my previous question was answered however i know that:

    2cos(x).cos(9x)

    has the derivative:

    -18cos(x)sin(9x) - 2sin(x)cos(9x)

    But will 2[cos1/2(f1-f2)t][cos1/2(f1+f2)t] have the same derivative?
    with f1= 10 and f2=8
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  2. #2
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    I believe it will.
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  3. #3
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    hrmmm. that makes it all seem a bit too easy then. i am meant to verify the answer from the first equation with that one. But to me they are basically the same.
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  4. #4
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    They are the same. Just find the derivavtive of the second to confirm.
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  5. #5
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    so from;
    y=2[cos1/2(10-8)x][cos1/2(10+8)x]
    = 2[cos1/2(2)x][cos1/2(18)x]
    =2cosx.cos(9x)

    then differentiate that and it should equal

    -18cos(x)sin(9x)-2sin(x)cos(9x)

    thats like two extra steps rofl.
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  6. #6
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    Exactly . You were using a previous result to help you with another. This will happen a lot in your studies.
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