Find `(dy)/(dx)` for `y=tan^(-1){sqrt((a-x)/(a+x))}," where " -a lt x lt a`

Explanation

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

### Step 1: Substitute \(x\)
Let \(x = a \cos \theta\). Then, we can rewrite \(y\) as:
\[ y = \tan^{-1}\left(\sqrt{\frac{a - a \cos \theta}{a + a \cos \theta}}\right) \]

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