Derivative of y=x⁴-12x+9

1. Differentiate $\left(x^{4} - 12 x\right) + 9$ term by term:

   1. Differentiate $x^{4} - 12 x$ term by term:

      1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$

      2. The derivative of a constant times a function is the constant times the derivative of the function.

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

         So, the result is: $-12$

      The result is: $4 x^{3} - 12$

   2. The derivative of the constant $9$ is zero.

   The result is: $4 x^{3} - 12$

The answer is:

$$4 x^{3} - 12$$