Show that the function given by `f(x)=(logx)/x`has maximum at `x = e`.

Explanation

To show that the function \( f(x) = \frac{\log x}{x} \) has a maximum at \( x = e \), we will follow these steps:

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

Using the quotient rule for differentiation, where if \( f(x) = \frac{u}{v} \), then \( f'(x) = \frac{u'v - uv'}{v^2} \).

Here, let:
- \( u = \log x \) (so \( u' = \frac{1}{x} \))
...