If `y=logsqrt((1+sin^(2)x)/(1-sinx))`, find `(dy)/(dx)`.

Explanation

To find \(\frac{dy}{dx}\) for the function \(y = \log\sqrt{\frac{1+\sin^2 x}{1-\sin x}}\), we will follow these steps:

### Step 1: Simplify the expression
We can rewrite the logarithmic expression using properties of logarithms:
\[ y = \log\sqrt{\frac{1+\sin^2 x}{1-\sin x}} = \frac{1}{2} \log\left(\frac{1+\sin^2 x}{1-\sin x}\right) \]

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