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

by RoRi

May 31, 2016

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

$F(t) = (\arcsin t, \arccos t).$

We compute

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

Stumbling Robot

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

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