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If y=|cosx|+|sinx|,then(dy/dx)"at"x=(2pi...

If `y=|cosx|+|sinx|,then(dy/dx)"at"x=(2pi)/3` is

A

`(1-sqrt(3))/(2)`

B

0

C

`(1)/(2)(sqrt(3)-1)`

D

none of these

Text Solution

Verified by Experts

In neighborhood of `x=(2pi)/(3),| cos x| = -cos x and | sin x| = som x`
`"or "y=-cos x+ sin x`
`therefore" "(dy)/(dx)=sin x + cos x`
Thus, at `x=(2pi)/(3)," we get "(dy)/(dx)= sin""(2pi)/(3)+cos""(2pi)/(3)=(sqrt(3)-1)/(2).`
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