If $y= |\sin x| + |\cos x|$, then $dy/dx$ at $x=2\pi/3$ is? If $$y= |\sin x| + |\cos x|,$$ 
then $dy/dx$ at $x = 2\pi/3$ is?          
Ans: $(\sqrt{3} - 1)/2$
How can we differentiate modulus functions? Can anyone explain? 

Since $\sin \frac {2\pi}3=\frac {\sqrt 3}2, |\sin \frac {2\pi}3|=\frac {\sqrt 3}2$  As the functions are continuous, the sign will not change nearby.  Just evaluate each one at $x=\frac {2\pi}3$, decide whether the value is positive or negative near there, and resolve the absolute value bars appropriately.
