Let `f(x)=tan^(-1)(g(x))` , where `g(x)` is monotonically increasing for `0

Explanation

To determine whether the function \( f(x) = \tan^{-1}(g(x)) \) is increasing or decreasing on the interval \( (0, \frac{\pi}{2}) \), we will analyze the derivative of \( f(x) \).

### Step 1: Find the derivative of \( f(x) \)

The derivative of \( f(x) \) can be calculated using the chain rule. The derivative of \( \tan^{-1}(u) \) with respect to \( u \) is given by:

\[
\frac{d}{du} \tan^{-1}(u) = \frac{1}{1 + u^2}
...