The differential coefficient of `f(log_e x) w.r.t. x,` where `f(x) = log_e x,` is (i) `x/lnx` (ii) `lnx/x` (iii) `1/(xlnx)` (iv) `xlnx`

Options

A. `(x)/(log_(e)x)`
B. `(1)/(x)log_(e)x`
C. `(1)/(xlog_(e)x)`
D. none of these

Explanation

To solve the problem, we need to find the differential coefficient of \( f(\log_e x) \) with respect to \( x \), where \( f(x) = \log_e x \).

### Step-by-Step Solution:

1. **Identify the Function**:
We have \( f(x) = \log_e x \). We need to find \( f(\log_e x) \).

2. **Substitute the Inner Function**:
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