Derivative of y=x-x³+x²+2

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

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

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

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

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

The answer is:

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