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    thinay's Avatar
    thinay Posts: 40, Reputation: 2
    Junior Member
     
    #1

    Aug 11, 2009, 04:22 AM
    derivatives of trigonometric functions
    please help me with this... :) Thanks in advance! When I tried to answer this last two numbers, the answer in the book with mine. And I think my answers are wrong. Here it is:

    1.) y = 1/2 x - 1/4 sin2x
    answer: sin^2 x
    2.) 2tan 1/2 x - x
    answer: tan^2 1/2 x
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #2

    Aug 11, 2009, 04:30 AM
    1.)
    answer:
    The derivative of is just 1/2.

    The derivative of sin(2x) is 2cos(2x)

    So, we have

    Which is an identity.
    thinay's Avatar
    thinay Posts: 40, Reputation: 2
    Junior Member
     
    #3

    Aug 11, 2009, 04:43 AM
    Oh.. I see.. my answer is correct which is 1-cos2x/2.. I just need to simplify it to get sin^2x..

    In #2, the answer that I got is sec^2 1/2 x.. Its wrong.
    galactus's Avatar
    galactus Posts: 2,271, Reputation: 282
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    #4

    Aug 11, 2009, 04:52 AM
    You're close about #2. You got sec, which is correct. Another identity.



    Don't forget that the derivative of x is 1.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #5

    Aug 11, 2009, 07:52 AM
    Quote Originally Posted by thinay View Post
    Oh.. i see.. my answer is correct which is 1-cos2x/2.. i just need to simplify it to get sin^2x..

    In #2, the answer that i got is sec^2 1/2 x.. its wrong.
    Ok, I don't know either that identity, but I do know that:



    So, just rearrange, you'll have:






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