If `f(x) = |cos x| + |sin x|`, then `dy/dx` at `x = (2pi)/3` is equal to

Options

A. `(1-sqrt(3))/(2)`
B. 0
C. `(1)/(2)(sqrt(3)-1)`
D. none of these

Explanation

To find the derivative \( \frac{dy}{dx} \) of the function \( f(x) = |\cos x| + |\sin x| \) at \( x = \frac{2\pi}{3} \), we will follow these steps:

### Step 1: Identify the quadrant
Since \( x = \frac{2\pi}{3} \) is in the second quadrant, we know that:
- \( \cos x \) is negative
- \( \sin x \) is positive

### Step 2: Rewrite the function
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