Derivative of y=4x^6-2x^4+3x^2+6

1. Differentiate $\left(3 x^{2} + \left(4 x^{6} - 2 x^{4}\right)\right) + 6$ term by term:

   1. Differentiate $3 x^{2} + \left(4 x^{6} - 2 x^{4}\right)$ term by term:

      1. Differentiate $4 x^{6} - 2 x^{4}$ 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: $x^{6}$ goes to $6 x^{5}$

            So, the result is: $24 x^{5}$

         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: $- 8 x^{3}$

         The result is: $24 x^{5} - 8 x^{3}$

      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: $6 x$

      The result is: $24 x^{5} - 8 x^{3} + 6 x$

   2. The derivative of the constant $6$ is zero.

   The result is: $24 x^{5} - 8 x^{3} + 6 x$

The answer is:

$$24 x^{5} - 8 x^{3} + 6 x$$