Derivative of 4x^3+3x

1. Differentiate $4 x^{3} + 3 x$ 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: $x^{3}$ goes to $3 x^{2}$

      So, the result is: $12 x^{2}$

   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: $3$

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

The answer is:

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