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

by RoRi

May 31, 2016

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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