Find the intervals in which the function f given by`f(x)=(4sinx-2x-x cos x)/(2+cos x)`is (i) increasing (ii) decreasing.

Explanation

To find the intervals in which the function \( f(x) = \frac{4 \sin x - 2x - x \cos x}{2 + \cos x} \) is increasing or decreasing, we will follow these steps:

### Step 1: Find the derivative \( f'(x) \)

Since \( f(x) \) is in the form of \( \frac{u}{v} \), we will use the quotient rule for differentiation:
\[ f'(x) = \frac{u'v - uv'}{v^2} \]
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