Derivative of 2x^4-4x^2+1

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

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

         So, the result is: $8 x^{3}$

      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: $- 8 x$

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

   2. The derivative of the constant $1$ is zero.

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

2. Now simplify:

   $$8 x \left(x^{2} - 1\right)$$

The answer is: