Derivative of (3x^4-2x+1)

1. Differentiate $3 x^{4} - 2 x + 1$ 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. The derivative of a constant times a function is the constant times the derivative of the function.

         1. Apply the power rule: $x$ goes to $1$

         So, the result is: $2$

      So, the result is: $-2$

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

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

The answer is:

$$12 x^{3} - 2$$