Derivative of 3x^4-4x^3+1

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

   1. Differentiate $3 x^{4} - 4 x^{3}$ 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: $x^{4}$ goes to $4 x^{3}$

         So, the result is: $12 x^{3}$

      2. 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: $- 12 x^{2}$

      The result is: $12 x^{3} - 12 x^{2}$

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

   The result is: $12 x^{3} - 12 x^{2}$

2. Now simplify:

   $$12 x^{2} \left(x - 1\right)$$

The answer is:

$$12 x^{2} \left(x - 1\right)$$