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Derivative of trig functions

  1. Mar 2, 2013 #1
    1. The problem statement, all variables and given/known data

    1. f(x) = 5 sin (8∏x)

    2. g(x) = 4∏ [ cos (3∏x) sin (3∏x)]

    3. h(x) = cos [sec (5∏x)]

    4. Sketch the graph of each function on the indicated interval, making use of relative extrema and points of inflection.

    f(x) = 2sinx + sin2x ; [0,2∏]


    3. The attempt at a solution

    1. f(x) = 5 sin (8∏x)

    f'(x) = 5 cos (8∏x) . (8∏)

    f'(x) = 40∏ cos (8∏x)[/COLOR]

    2. g(x) = 4∏ [ cos (3∏x) sin (3∏x)]

    g'(x) = 4∏ {[cos (3∏x)][(sin (3∏x)]' + [sin (3∏x)][cos (3∏x)]'}

    g'(x) = 4∏ {[cos (3∏x)][cos (3∏x) . 3∏ ] + [ sin (3∏x)][ -sin (3∏x) . 3∏ ]}

    g'(x) = 12∏ cos2 (3∏x) -12∏ sin2 (3∏x)

    3. h(x) = cos [sec(5∏x)]

    h'(x) = -sin [ sec(5∏x) . 5∏][ tan (5∏x) . 5∏]

    h'(x) = -25∏ sec (5∏x) tan(5∏x)[/COLOR]

    4. Sketch the graph of each function on the indicated interval, making use of relative extrema and points of inflection.

    f(x) = 2sinx + sin2x

    f'(x) = 2cosx + cos2x . 2

    f'(x) = 2cosx + 2cos(2x)

    => f'(x) = 0

    2cosx + 2cos(2x) = 0

    Now, how to proceed from here?
     
    Last edited by a moderator: Mar 2, 2013
  2. jcsd
  3. Mar 2, 2013 #2

    tiny-tim

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    hi domyy! :smile:

    1 is ok

    2 is ok, except haven't you lost one of the ∏s ?

    3 is almost completely wrong, have another go, writing it out more carefully at each step

    4 now you need to use one of the standard trigonometric identities (cosA - cosB), all of which you should learn :wink:
     
  4. Mar 2, 2013 #3
    :shy: Hi!

    3. h(x) = cos [sec(5∏x)]

    h'(x) = -sin [ sec(5∏x)][ tan (5∏x)] . 5∏

    h'(x) = -5∏sin [ sec (5∏x) tan(5∏x)]

    How about now?

    What's the wrong with ∏ on nr 2 ? :/
     
    Last edited by a moderator: Mar 2, 2013
  5. Mar 2, 2013 #4
    I received a warning for excessive use of colors ??

    I thought it was actually better for whoever was reading..to separate each problem by color since I was posting more than one.

    I didn't do it because I was trying to decorate my post.

    My bad.
     
    Last edited: Mar 2, 2013
  6. Mar 2, 2013 #5

    tiny-tim

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    hi domyy! :smile:

    (btw, i didn't complain about the colours, but i didn't like them)

    3 is now ok, except the derivative of sec is tan2 :redface:

    (and, for 2, 4∏*3∏ = 12∏2 :wink:)
     
  7. Mar 2, 2013 #6
    Yes. Got it!!
    =)

    Now, I'm gonna work on nr. 4
     
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