Derivative of f(x)=3x³-4x²

1. Differentiate $3 x^{3} - 4 x^{2}$ 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: $9 x^{2}$

   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: $8 x$

      So, the result is: $- 8 x$

   The result is: $9 x^{2} - 8 x$

2. Now simplify:

   $$x \left(9 x - 8\right)$$

The answer is:

$$x \left(9 x - 8\right)$$