d/dx(1 + 2 x - x^2)

Differentiate the sum term by term and factor out constants:

= d/dx(1) + 2 (d/dx(x)) - d/dx(x^2)

The derivative of 1 is zero:

= 2 (d/dx(x)) - d/dx(x^2) + 0

Simplify the expression:

= 2 (d/dx(x)) - d/dx(x^2)

The derivative of x is 1:

= -(d/dx(x^2)) + 1 2

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.

d/dx(x^2) = 2 x:

Answer: |

| = 2 - 2 x