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y = cos ^(-1)((1 - x^(2))/(1+ x^(2))) 0 ...

`y = cos ^(-1)((1 - x^(2))/(1+ x^(2))) 0 lt x lt 1`

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To solve the problem \( y = \cos^{-1}\left(\frac{1 - x^2}{1 + x^2}\right) \) for \( 0 < x < 1 \) and find \( \frac{dy}{dx} \), we will follow these steps: ### Step 1: Substitute \( x \) with \( \tan(\theta) \) Let \( x = \tan(\theta) \). This substitution will help us simplify the expression involving the inverse cosine function. ### Step 2: Rewrite \( y \) in terms of \( \theta \) Using the identity for tangent, we can rewrite: \[ ...
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