Derivative of cos(x)-log(x)

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

   1. The derivative of cosine is negative sine:

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

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

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

      So, the result is: $- \frac{1}{x}$

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

The answer is:

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