Differentiate the following function with respect to `x :` `cos^(-1){2xsqrt(1-x^2)},1/(sqrt(2))`

Explanation

To differentiate the function \( y = \cos^{-1}(2x\sqrt{1-x^2}) \) with respect to \( x \) for \( \frac{1}{\sqrt{2}} < x < 1 \), we can follow these steps:

### Step 1: Substitute \( x = \sin(\theta) \)
Let \( x = \sin(\theta) \). Then, we have:
\[ \sqrt{1 - x^2} = \sqrt{1 - \sin^2(\theta)} = \cos(\theta) \]
Thus, the function becomes:
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