Derivative of lnx-sinx

1. Differentiate $\log{\left(x \right)} - \sin{\left(x \right)}$ 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. The derivative of sine is cosine:

         $$\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$$

      So, the result is: $- \cos{\left(x \right)}$

   The result is: $- \cos{\left(x \right)} + \frac{1}{x}$

The answer is:

$$- \cos{\left(x \right)} + \frac{1}{x}$$