Derivative of -x^2+2x+1

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

   1. Differentiate $- x^{2} + 2 x$ term by term:

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

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

         So, the result is: $- 2 x$

      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: $2$

      The result is: $2 - 2 x$

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

   The result is: $2 - 2 x$

The answer is:

$$2 - 2 x$$