Derivative of 4x^2+12x+9

1. Differentiate $\left(4 x^{2} + 12 x\right) + 9$ term by term:

   1. Differentiate $4 x^{2} + 12 x$ 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: $x^{2}$ goes to $2 x$

         So, the result is: $8 x$

      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: $8 x + 12$

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

   The result is: $8 x + 12$

The answer is:

$$8 x + 12$$