Q. If $y = \cos^{- 1}{(\cos{x),\ }\ then\frac{dy}{dx}}$ is
A) 1 in the whole plane
B) $- 1$ in the whole plane
C) 1 in the 2^{nd} and 3^{rd} quadrants of the plane
D) $- 1$ in the 3^{rd} and 4^{th} quadrants of the plane
Explanation
(d)
Given, $y = \cos^{- 1}{\cos x}$
For $\leq x \leq \pi,y = x$
$\Rightarrow \ \ \frac{dy}{dx} = 1$
For $\pi < x \leq 2\pi,\ y = \cos^{- 1}{cos(2\pi - x)}$
$\Rightarrow \ \ y = \ - x$
$\Rightarrow \ \ \ \frac{dy}{dx} = \ - 1$
Hence, option (d) is correct.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.