Derivative of x^4-2x^3

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

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

   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: $x^{3}$ goes to $3 x^{2}$

         So, the result is: $6 x^{2}$

      So, the result is: $- 6 x^{2}$

   The result is: $4 x^{3} - 6 x^{2}$

2. Now simplify:

   $$x^{2} \cdot \left(4 x - 6\right)$$

The answer is:

$$x^{2} \cdot \left(4 x - 6\right)$$