Derivative of 2x^3-6x+1

1. Differentiate $\left(2 x^{3} - 6 x\right) + 1$ term by term:

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

         So, the result is: $-6$

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

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

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

The answer is:

$$6 x^{2} - 6$$