Derivative of y=6x^3+2x-3

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

   1. Differentiate $6 x^{3} + 2 x$ 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: $18 x^{2}$

      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: $2$

      The result is: $18 x^{2} + 2$

   2. The derivative of the constant $-3$ is zero.

   The result is: $18 x^{2} + 2$

The answer is:

$$18 x^{2} + 2$$