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

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

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

The answer is:

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