Derivative of x^3-12x+1

1. Differentiate $\left(x^{3} - 12 x\right) + 1$ term by term:

   1. Differentiate $x^{3} - 12 x$ term by term:

      1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

      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: $-12$

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

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

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

The answer is:

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