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To find \( \frac{d}{dx} \) of the given function \( y = x \sin^{-1}x + \sqrt{1-x^2} \), we need to use the sum rule and the chain rule of differentiation.

Let's break down the function into its individual components:

1. \( x \sin^{-1}x \)
2. \( \sqrt{1-x^2} \)

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