Derivative of cosx-2x+4

1. Differentiate $\left(- 2 x + \cos{\left(x \right)}\right) + 4$ term by term:

   1. Differentiate $- 2 x + \cos{\left(x \right)}$ 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. Apply the power rule: $x$ goes to $1$

         So, the result is: $-2$

      The result is: $- \sin{\left(x \right)} - 2$

   2. The derivative of the constant $4$ is zero.

   The result is: $- \sin{\left(x \right)} - 2$

The answer is:

$$- \sin{\left(x \right)} - 2$$