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)

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

According to question,
$|\cos x|=-\cos x$
$|\sin x|=\sin x$
$\therefore \frac{dy}{dx}=\sin x+\cos x$
$\therefore {\left(\frac{dy}{dx}\right)}_{\frac{2\pi }{3}}=\frac{\sqrt{3}}{2}-\frac{1}{2}=\frac{\sqrt{3}-1}{2}$.