Show that `f(x)=1/(1+x^2)` decreases in the interval `[0,\ oo)` and increases in the interval `(-oo,\ 0]` .

Explanation

To show that the function \( f(x) = \frac{1}{1+x^2} \) decreases in the interval \([0, \infty)\) and increases in the interval \((- \infty, 0]\), we will follow these steps:

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

\[ f(x) = \frac{1}{1+x^2} \]
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