Derivative of cosx+12x

1. Differentiate $12 x + \cos{\left(x \right)}$ 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: $12$

   The result is: $12 - \sin{\left(x \right)}$

The answer is:

$$12 - \sin{\left(x \right)}$$