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

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

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

      1. Differentiate $x^{4} - 3 x^{2}$ term by term:

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

         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: $4 x^{3} - 6 x$

      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: $4 x^{3} - 6 x - 2$

   2. The derivative of the constant $-4$ is zero.

   The result is: $4 x^{3} - 6 x - 2$

The answer is:

$$4 x^{3} - 6 x - 2$$