If ` y = tan ^-1[x/(1+sqrt(1-x^2))] "then find" dy/dx`

Explanation

To find the derivative \( \frac{dy}{dx} \) for the function \( y = \tan^{-1} \left( \frac{x}{1 + \sqrt{1 - x^2}} \right) \), we can follow these steps:

### Step-by-Step Solution:

1. **Substitution**:
We start by substituting \( x = \sin \theta \). This gives us:
\[
y = \tan^{-1} \left( \frac{\sin \theta}{1 + \sqrt{1 - \sin^2 \theta}} \right)
...