Derivative of 2x³-x²+4-2

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

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

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

         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: $- 2 x$

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

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

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

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

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

2. Now simplify:

   $$2 x \left(3 x - 1\right)$$

The answer is:

$$2 x \left(3 x - 1\right)$$