Question

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

• A. $\frac{1}{2}\left(\sqrt{3}+1\right)$
• B. $2\left(\sqrt{3}-1\right)$
• C. $\frac{1}{2}\left(\sqrt{3}-1\right)$
• D. none of these

Answer 1

The correct option is A $\frac{1}{2}\left(\sqrt{3}+1\right)$

$y=|\cos x|+|\sin x|$

at $x=\frac{2\pi }{3},$

$y=-\cos x+\sin x$

$now,\frac{dy}{dx}=\sin x+\cos x$

$\frac{dy}{dx}=\sin \frac{2\pi }{3}+\cos \frac{2\pi }{3}$

$\frac{dy}{dx}=\frac{\sqrt{3}}{2}+\frac{1}{2}$

$\frac{dy}{dx}=\frac{1}{2}(\sqrt{3}+1)$