Show that the maximum value of `(1/x)^x` is `e^(1//e)` .

Explanation

To show that the maximum value of \( f(x) = \left( \frac{1}{x} \right)^x \) is \( e^{\frac{1}{e}} \), we will follow these steps:

### Step 1: Rewrite the function
We start with the function:
\[ f(x) = \left( \frac{1}{x} \right)^x = x^{-x} \]
To simplify the differentiation process, we take the natural logarithm of both sides:
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