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Math Help - Find the second derivative

  1. #1
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    Find the second derivative

    x=4sin(t) and y=2cos(t). I found the first derivative to be -(1/2)tan(t). How do I find the second derivative?
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  2. #2
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    Your first derivative is fine. To find the second derivative take the derivative of the the first derivative. It's a standard derivative \dfrac{1}{2} \cdot \dfrac{d}{dt} \tan(t) = \dfrac{1}{2} \sec^2(t)
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    \displaystyle \frac{d^2y}{dx^2}= \frac{d}{dx}\frac{dy}{dx} = \frac{d}{dt}\frac{dy}{dx}\frac{dt}{dx}
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  4. #4
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    Quote Originally Posted by boosays View Post
    x=4sin(t) and y=2cos(t). I found the first derivative to be -(1/2)tan(t). How do I find the second derivative?
    \displaystyle \frac{d}{dx} \left(\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\right) = \frac{d}{dt} \left(\frac{\frac{dy}{dx}}{\frac{dx}{dt}}\right)

    \displaystyle \frac{d}{dt} \left(\frac{-\tan{t}}{8\cos{t}}\right)

    do the quotient rule to finish ...
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