Discuss the differentiability of `f(x)=|(log)_e x| x > 0.`

Explanation

To discuss the differentiability of the function \( f(x) = |\log_e x| \) for \( x > 0 \), we can follow these steps:

### Step 1: Understand the Function
The function \( f(x) = |\log_e x| \) involves the natural logarithm of \( x \) and the absolute value. The natural logarithm, \( \log_e x \), is defined for \( x > 0 \) and has specific behavior:
- \( \log_e x < 0 \) when \( 0 < x < 1 \)
- \( \log_e x = 0 \) when \( x = 1 \)
- \( \log_e x > 0 \) when \( x > 1 \)

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