Derivative of 2x^3-3x^2+1

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

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

      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: $- 6 x$

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

   2. The derivative of the constant $1$ is zero.

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

2. Now simplify:

   $$6 x \left(x - 1\right)$$

The answer is: