Derivative of y=(x^2-3x+3)(x^2+2x-1)

1. Apply the product rule:

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

   $f{\left(x \right)} = x^{2} - 3 x + 3$; to find $\frac{d}{d x} f{\left(x \right)}$:

   1. Differentiate $x^{2} - 3 x + 3$ 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: $3$

         So, the result is: $-3$

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

      The result is: $2 x - 3$

   $g{\left(x \right)} = x^{2} + 2 x - 1$; to find $\frac{d}{d x} g{\left(x \right)}$:

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

      3. The derivative of the constant $\left(-1\right) 1$ is zero.

      The result is: $2 x + 2$

   The result is: $\left(2 x - 3\right) \left(x^{2} + 2 x - 1\right) + \left(2 x + 2\right) \left(x^{2} - 3 x + 3\right)$

2. Now simplify:

   $$4 x^{3} - 3 x^{2} - 8 x + 9$$

The answer is:

$$4 x^{3} - 3 x^{2} - 8 x + 9$$