Derivative of y=x+2cosx

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

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

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

      1. The derivative of cosine is negative sine:

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

      So, the result is: $- 2 \sin{\left(x \right)}$

   The result is: $1 - 2 \sin{\left(x \right)}$

The answer is:

$$1 - 2 \sin{\left(x \right)}$$