Discuss maxima/minima of `f(x) = (x)/(1 + x tan x), x in (0, (pi)/(2))`

Explanation

To discuss the maxima and minima of the function \( f(x) = \frac{x}{1 + x \tan x} \) for \( x \in (0, \frac{\pi}{2}) \), we will follow these steps:

### Step 1: Differentiate the function
First, we need to find the derivative of the function \( f(x) \).

\[ f'(x) = \frac{(1 + x \tan x) \cdot (1) - x \cdot \frac{d}{dx}(1 + x \tan x)}{(1 + x \tan x)^2} \]
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