Derivative of x²+2x-1⁴

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

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

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

      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: $2 x + 2$

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

   The result is: $2 x + 2$

The answer is:

$$2 x + 2$$