`tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lt a`

Explanation

To solve the problem \( y = \tan^{-1} \left( \frac{x}{\sqrt{a^2 - x^2}} \right) \) where \( |x| < a \), we will use a substitution method. Here are the steps:

### Step-by-Step Solution:

1. **Set the Expression Equal to y**:
\[ y = \tan^{-1} \left( \frac{x}{\sqrt{a^2 - x^2}} \right) \]
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