Derivative of x⁴-2x²-1

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

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

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

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

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

2. Now simplify:

   $$4 x \left(x^{2} - 1\right)$$

The answer is:

$$4 x \left(x^{2} - 1\right)$$