Derivative of 2-x-x^3

1. Differentiate $- x^{3} + \left(2 - x\right)$ term by term:

   1. Differentiate $2 - x$ term by term:

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

      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: $-1$

      The result is: $-1$

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

      1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

      So, the result is: $- 3 x^{2}$

   The result is: $- 3 x^{2} - 1$

The answer is:

$$- 3 x^{2} - 1$$