Mathematics

Problem

For

-1<x<1

, the identity

\arcsin x+\arccos x=\dfrac{\pi}{2}

is true. Which of the following conclusions about their derivatives on this interval is most consistent with the identity? a)

\displaystyle \frac{d}{dx}\arcsin x=\frac{d}{dx}\arccos x

\displaystyle \frac{d}{dx}\arcsin x+\frac{d}{dx}\arccos x=\frac{\pi}{2}

\displaystyle \frac{d}{dx}\arcsin x=-\,\frac{d}{dx}\arccos x

\displaystyle \frac{d}{dx}\arcsin x=\frac{1}{\arccos x}