Differentiate `logsqrt((1+cos^(2)x)/((1-e^(2x))))` w.r.t. x.

Explanation

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

### Step 1: Rewrite the Function
First, we can simplify the expression using logarithmic properties. Recall that \( \log\sqrt{a} = \frac{1}{2} \log a \). Thus, we can rewrite \( y \) as:

\[ y = \frac{1}{2} \log\left(\frac{1 + \cos^2 x}{1 - e^{2x}}\right) \]
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