Question

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

• A. $\frac{1}{2}(\sqrt{3}+1)$
• B. $2(\sqrt{3}-1)$
• C. $\frac{1}{2}(\sqrt{3}-1)$
• D. $\frac{1}{4}(\sqrt{3}-1)$

Answer 1

The correct option is C

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

Since $\sin x$ is positive and $\cos x$ is negative in the second quadrant, $y=-\cos x+\sin x$
$\Rightarrow \frac{dy}{dx}=\sin x+\cos x$
$\frac{dy}{dx}\text{at}\frac{2\pi }{3}=\frac{1}{2}(\sqrt{3}-1)$