Derivative of -x^4+8*x^2-16

1. Differentiate $\left(- x^{4} + 8 x^{2}\right) - 16$ term by term:

   1. Differentiate $- x^{4} + 8 x^{2}$ 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: $- 4 x^{3}$

      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: $16 x$

      The result is: $- 4 x^{3} + 16 x$

   2. The derivative of the constant $-16$ is zero.

   The result is: $- 4 x^{3} + 16 x$

2. Now simplify:

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

The answer is:

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