Derivative of e^x*(x^2-2*x+2)

1. Apply the product rule:

   $$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$$

   $f{\left(x \right)} = e^{x}$; to find $\frac{d}{d x} f{\left(x \right)}$:

   1. The derivative of $e^{x}$ is itself.

   $g{\left(x \right)} = x^{2} - 2 x + 2$; to find $\frac{d}{d x} g{\left(x \right)}$:

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

         So, the result is: $-2$

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

      The result is: $2 x - 2$

   The result is: $\left(2 x - 2\right) e^{x} + \left(x^{2} - 2 x + 2\right) e^{x}$

2. Now simplify:

   $$x^{2} e^{x}$$

The answer is:

$$x^{2} e^{x}$$