Derivative of x⁴+2x²

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. Now simplify:

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

The answer is:

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