If `y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],`find`(dy)/(dx)`

Explanation

To find the derivative of the function \( y = \sin\left[2 \tan^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right] \), we will follow these steps:

### Step 1: Simplify the expression inside the sine function
We start with the expression:
\[ y = \sin\left[2 \tan^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right)\right] \]
Using the identity for tangent, we know that:
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