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

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

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

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

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

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

2. Now simplify:

   $$3 x \left(2 - x\right)$$

The answer is: