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Math Help - Differentiation

  1. #1
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    Differentiation

    I am having a problem with these two questions

    1) f(t) =(3t-2) sin2t

    2) f(theta) = 2cos(3theta-1)/3 theta

    Help would be appreciated
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Jaffa View Post
    I am having a problem with these two questions

    1) f(t) =(3t-2) sin2t

    2) f(theta) = 2cos(3theta-1)/3 theta

    Help would be appreciated
    OK but ... what is the question you are supposed to answer ?
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  3. #3
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    Sorry, did not make myself clear,I have to differentiate the functions
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  4. #4
    Member Mentia's Avatar
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    The first question is an application of the product rule, the second is an application of the quotient rule. Check them out in your book.
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  5. #5
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    Quote Originally Posted by Jaffa View Post
    I am having a problem with these two questions

    1) f(t) =(3t-2) sin2t

    2) f(theta) = 2cos(3theta-1)/3 theta

    Help would be appreciated
    f(t) = (3t - 2) * sin (2t)
    Using the product and chain rules:

    f'(t) = (3t - 2) * 2 cos (2t) + sin (2t) * 3
    f'(t) = 2*(3t - 2) cos (2t) + 3 sin (2t)

    f(\theta) = \frac{2 cos (3\theta -1)}{3\theta}
    Using the chain rule and quotient rule:
    f'(\theta) = \frac{3\theta * -6 sin (3\theta-1) - 6 cos (3\theta-1)}{(3\theta)^2}
    f'(\theta) = \frac{-18\theta * sin (3\theta-1) - 6 cos (3\theta-1)}{9\theta^2}
    f'(\theta) = \frac{-6\theta * sin (3\theta-1) - 2 cos (3\theta-1)}{3\theta^2}
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