Question

If $y = |\cos x| + |\sin x|$ then $\frac{dy}{dx}$ at $x = \frac{2\pi}{3}$ is

• A. $\frac{1 - \sqrt{3}}{2}$
• B. 0
• C. $\frac{1}{2}(\sqrt{3} - 1)$
• D. None of these

Answer 1

Answer: (C)

$\frac{1}{2}(\sqrt{3} - 1)$

Answer 2

Around $x = \frac{2\pi}{3},$ $|\cos x| = - \cos x$ and $|\sin x| = \sin x$

$\therefore$ $y = - \cos x + \sin x$ $\therefore$ $\frac{dy}{dx} = \sin x + \cos x$

At $x = \frac{2\pi}{3}$, $\frac{dy}{dx} = \sin\frac{2\pi}{3} + \cos\frac{2\pi}{3}$ = $\frac{\sqrt{3}}{2} - \frac{1}{2} = \frac{1}{2}(\sqrt{3} - 1)$.