Derivative of y=4+6x-3x^4

1. Differentiate $- 3 x^{4} + \left(6 x + 4\right)$ term by term:

   1. Differentiate $6 x + 4$ term by term:

      1. The derivative of the constant $4$ 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: $6$

      The result is: $6$

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

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

      So, the result is: $- 12 x^{3}$

   The result is: $6 - 12 x^{3}$

The answer is:

$$6 - 12 x^{3}$$