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Compute derivatives of F(t) = (cos t, sin2 t, sin (2t), tan t)

Compute the derivatives F'(t) and F''(t) of the vector valued function

    \[ F(t) = (\cos t, \sin^2 t, \sin 2t, \tan t). \]


We compute

    \begin{align*}  F'(t) &= (-\sin t, \sin 2t, 2 \cos 2t, \sec^2 t) \\  F''(t) &= (-\cos t, 2 \cos 2t, -4 \sin 2t, 2 \sec^2 t \tan t).  \end{align*}

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