if `y= (sin ^(-1)x)/(sqrt(1-x^2))` then prove that `(1-x)^2) .d/dx=xy+1`

Explanation

To prove that \( (1 - x^2) \frac{dy}{dx} = xy + 1 \) given that \( y = \frac{\sin^{-1} x}{\sqrt{1 - x^2}} \), we will differentiate \( y \) with respect to \( x \) and manipulate the expression accordingly.

### Step-by-Step Solution:

1. **Given Function**:
\[ y = \frac{\sin^{-1} x}{\sqrt{1 - x^2}} \]
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