Show that `f(x)=1/x` is a decreasing function on `(0,\ oo)` .

Explanation

To show that the function \( f(x) = \frac{1}{x} \) is a decreasing function on the interval \( (0, \infty) \), we can follow these steps:

### Step 1: Find the derivative of the function
We start by differentiating the function \( f(x) \):
\[ f'(x) = \frac{d}{dx} \left( \frac{1}{x} \right) \]
Using the power rule, we can rewrite \( \frac{1}{x} \) as \( x^{-1} \):
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