For , the identity is true. Which of the following conclusions about their…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

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

(b)

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

(c)

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

(d)

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