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Math Help - differentiate

  1. #1
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    differentiate

    hmmm i think im doing it correctly but im not quite sure and i dont know how to simplify trig terms...help please...


    (5 - cos x) / (5 + sin x)

    I got this far by using the quotient rule...am i correct so far???
    --->  (sin x( 5 + sinx) - (5-cos x)cos x ) / 5 + sin^2x


    Also another question......

    Find f'
    f(x) = sin^2 x + cos^2 x


    i got ....  2 sin x . cos x + 2 cos x . -sin x

    correct??

    how would i simplify it?
    Last edited by b00yeah05; February 16th 2008 at 12:20 AM. Reason: fixed errors and added question
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  2. #2
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    Quote Originally Posted by b00yeah05 View Post
    hmmm i think im doing it correctly but im not quite sure and i dont know how to simplify trig terms...help please...

    (5 - cos x) / (5 + sin x)

    I got this far by using the quotient rule...am i correct so far???
    --->  (sin x( 5 + sinx) - (5-cos x)cos x ) / 5 + sin^2x

    Also another question......
    Find f'
    f(x) = sin^2 x + cos^2 x
    i got ....  2 sin x . cos x + 2 cos x . -sin x
    #1: Expand the brackets in the numerator. The denominator should read (5+\sin(x))^2

    #2. If the wording of this question is correct then someone has made a practical joke:

    Since (\sin(x))^2 + (\cos(x))^2 = 1 the first derivative should be zero:

    f'(x)=2\sin(x) \cdot \cos(x) + 2(-\sin(x)) \cdot \cos(x) = 2\sin(x) \cdot \cos(x) - 2\sin(x) \cdot \cos(x) = 0
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