Derivative of y=-x^3-6x^2+2x+1

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

   1. The derivative of a constant times a function is the constant times the derivative of the function.

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

      So, the result is: $- 3 x^{2}$

   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: $12 x$

      So, the result is: $- 12 x$

   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: $2$

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

   The result is: $- 3 x^{2} - 12 x + 2$

The answer is:

$$- 3 x^{2} - 12 x + 2$$