Find the intervals on which the function `f(x) = (x)/((x^(2) +1))` is (a) increasing (b) decreasing

Explanation

To find the intervals on which the function \( f(x) = \frac{x}{x^2 + 1} \) is increasing or decreasing, we will follow these steps:

### Step 1: Find the derivative of the function
To determine where the function is increasing or decreasing, we first need to find its derivative \( f'(x) \).

Using the quotient rule, where \( u = x \) and \( v = x^2 + 1 \):
\[
f'(x) = \frac{v \cdot u' - u \cdot v'}{v^2}
...