Derivative of lnx-x

1. Differentiate $- x + \log{\left(x \right)}$ term by term:

   1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$.

   2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: $x$ goes to $1$

      So, the result is: $-1$

   The result is: $-1 + \frac{1}{x}$

2. Now simplify:

   $$\frac{1 - x}{x}$$

The answer is:

$$\frac{1 - x}{x}$$