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Math Help - Derivatives involving trigonometry

  1. #1
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    Derivatives involving trigonometry

    "Given y=2sin2t and x=5cos4t, determine dy/dx."

    I know I have to use the chain rule here by:

    dy/dx = dy/dt x dt/dx
    but I'm not sure how to isolate dy/dt and dt/dx.

    Please help.
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  2. #2
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    Quote Originally Posted by Melnarie View Post
    "Given y=2sin2t and x=5cos4t, determine dy/dx."

    I know I have to use the chain rule here by:

    dy/dx = dy/dt x dt/dx
    but I'm not sure how to isolate dy/dt and dt/dx.

    Please help.
    There's a slightly easier way.
    y = 2 sin(2t) ==> \frac{dy}{dt} = 2 cos(2t) \cdot 2 = 4 cos(2t)

    x = 5 cos(4t) ==> \frac{dx}{dt} = 5 \cdot -sin(4t) \cdot 4 = -20 sin(4t)

    Thus
    \frac{dy}{dx} = \frac{ \left ( \frac{dy}{dt} \right ) }{  \left ( \frac{dx}{dt} \right ) }

    \frac{dy}{dx} = \frac{4 cos(2t)}{-20 sin(4t)} = - \frac{cos(2t)}{5sin(4t)}

    -Dan
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  3. #3
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    oooh! thanks so much!!
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