Derivative of y=(x³-3x²+x)¹¹

1. Let $u = x + \left(x^{3} - 3 x^{2}\right)$.

2. Apply the power rule: $u$ goes to $1$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + \left(x^{3} - 3 x^{2}\right)\right)$:

   1. Differentiate $x + \left(x^{3} - 3 x^{2}\right)$ term by term:

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

         1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

         2. 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: $- 6 x$

         The result is: $3 x^{2} - 6 x$

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

      The result is: $3 x^{2} - 6 x + 1$

   The result of the chain rule is:

   $$3 x^{2} - 6 x + 1$$

The answer is:

$$3 x^{2} - 6 x + 1$$