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Compute derivatives of F(t) = (arcsin t, arccos t)

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

    \[ F(t) = (\arcsin t, \arccos t). \]


We compute

    \begin{align*}  F'(t) &= \left( \frac{1}{\sqrt{1-t^2}}, \frac{-1}{\sqrt{1-t^2}} \right) \\  F''(t) &= \left( \frac{t}{(1+t^2)^{\frac{3}{2}}}, \frac{-t}{(1+t^2)^{\frac{3}{2}}} \right). \end{align*}

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