Derivative of -x^3+4*x^2-4*x

1. Differentiate $- 4 x + \left(- x^{3} + 4 x^{2}\right)$ term by term:

   1. Differentiate $- x^{3} + 4 x^{2}$ 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. Apply the power rule: $x^{2}$ goes to $2 x$

         So, the result is: $8 x$

      The result is: $- 3 x^{2} + 8 x$

   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: $-4$

   The result is: $- 3 x^{2} + 8 x - 4$

The answer is:

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