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y = sin ^(-1)(2xsqrt(1 - x^(2))),-(1)/sq...

`y = sin ^(-1)(2xsqrt(1 - x^(2))),-(1)/sqrt(2) lt x lt (1)/sqrt(2)`

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To solve the problem of finding the derivative of the function \( y = \sin^{-1}(2x\sqrt{1 - x^2}) \) for \( -\frac{1}{\sqrt{2}} < x < \frac{1}{\sqrt{2}} \), we will follow these steps: ### Step 1: Rewrite the function We start with the function: \[ y = \sin^{-1}(2x\sqrt{1 - x^2}) \] ...
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