Derivative of y=x³-3x²+3x+1

1. Differentiate $x^{3} - 3 x^{2} + 3 x + 1$ 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. 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: $6 x$

      So, the result is: $- 6 x$

   3. 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: $3$

   4. The derivative of the constant $1$ is zero.

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

The answer is:

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