Derivative of 5+12x-x^3

1. Differentiate $- x^{3} + \left(12 x + 5\right)$ term by term:

   1. Differentiate $12 x + 5$ term by term:

      1. The derivative of the constant $5$ is zero.

      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: $12$

   2. 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: $- 3 x^{2}$

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

The answer is:

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