Answer
$$1-\ln x.
$$
Work Step by Step
$$
\left|\begin{array}{rrr}{x} & {\ln x} \\ {1} & {\frac{1}{x}} \end{array}\right|=(x)(1/x)-\ln x=1-\ln x.
$$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.