If `y=(xsin^(-1)x)/(sqrt(1-x^2))+logsqrt(1-x^2)` , then prove that `(dy)/(dx)=(sin^(-1)x)/((1-x^2)^(3/2))`

Explanation

To prove that \(\frac{dy}{dx} = \frac{\sin^{-1} x}{(1 - x^2)^{3/2}}\) for the function

\[ y = \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} + \log \sqrt{1 - x^2}, \]

we will differentiate \(y\) with respect to \(x\) step by step.

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