Derivative of 12*x^3+6*x^2-42

1. Differentiate $\left(12 x^{3} + 6 x^{2}\right) - 42$ term by term:

   1. Differentiate $12 x^{3} + 6 x^{2}$ 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: $36 x^{2}$

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

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

         So, the result is: $12 x$

      The result is: $36 x^{2} + 12 x$

   2. The derivative of the constant $-42$ is zero.

   The result is: $36 x^{2} + 12 x$

2. Now simplify:

   $$12 x \left(3 x + 1\right)$$

The answer is:

$$12 x \left(3 x + 1\right)$$