If`y=(sinx/2+cosx/2)^2,`fin ``d`(dy)/(dx)a tx=pi/6`

Explanation

To find the derivative of the function \( y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 \) and evaluate it at \( x = \frac{\pi}{6} \), we will follow these steps:

### Step 1: Rewrite the function
We start with the function:
\[ y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 \]

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