The derivative of the function `cot^(-1){(cos2"x")^(1/2)}a tx=pi/6` is `(2/3)^(1/2)` (b) `(1/3)^(1/2)` (c) `3^(1/2)` (d) `6^(1/2)`

Explanation

To solve the problem of finding the derivative of the function \( y = \cot^{-1}(\sqrt{\cos(2x)}) \) at \( x = \frac{\pi}{6} \), we will follow these steps:

### Step 1: Define the function
Let
\[ y = \cot^{-1}(\sqrt{\cos(2x)}) \]

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