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Math Help - differentiate the trig function

  1. #1
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    differentiate the trig function

    I need to differentiate this function:
    secx^2-tanx^2+cosx. these are my steps:
    f'(x)= secx^2*tanx^2-secx^2-sinx and do not know how to finish this but i know the first two terms are suppose to cancel. the answer is suppose to be -sin x.

    And also, How does 2 sinx cosx translate to sin2x?
    Last edited by driver327; July 14th 2007 at 11:36 AM. Reason: forgot a question
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by driver327 View Post
    I need to differentiate this function:
    secx^2-tanx^2+cosx. these are my steps:
    f'(x)= secx^2*tanx^2-secx^2-sinx and do not know how to finish this but i know the first two terms are suppose to cancel. the answer is suppose to be -sin x.
    I dont know if this is right, please double check it.

     sec^2 x - tan^2 x + cos x

     \frac{dy}{dx} = (2 sec x)(sec x \ tan x) - (2 tan x)( sec^2 x ) - (sin x)

      = \frac{2 sin x}{cos^3 x} - \frac{2 sin x}{cos^3 x} - (sin x)

      =  - sin x
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by driver327 View Post

    And also, How does 2 sinx cosx translate to sin2x?
    That's a long proof. Please PM me about that. I need to find it somewhere in my book.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by driver327 View Post
    How does 2 sinx cosx translate to sin2x?
    Use the addition formula for sine.


    \sin 2x = \sin (x + x)

    = \sin x \cos x + \sin x \cos x

    = 2 \sin x \cos x
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  5. #5
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Jhevon View Post
    Use the addition formula for sine.


    \sin 2x = \sin (x + x)

    = \sin x \cos x + \sin x \cos x

    = 2 \sin x \cos x
    I thought he wanted the full proof...

    In school we make use of Pythagoras and the distance formula to prove it.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by janvdl View Post
    I thought he wanted the full proof...

    In school we make use of Pythagoras and the distance formula to prove it.
    i don't think so. the question he asked was for a derivative, so i assume he wanted to know why someone would go between 2sin(x)cos(x) and sin(2x) to take a derivative (taking the derivative of the latter is much easier), so i didn't think a full proof was needed since it would just be an intermediate step for finding a derivative or something. besides, the wording he used kind of hinted he wasn't after a proof. he would more likely use the word "show" or "prove" or "proof" if he was after that
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  7. #7
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    Just to clear the confusion, i just wanted to see how one trig function turns into another. Jhevon was right.
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