Derivative of y=x^5+5x^4-10x^2+6

1. Differentiate $x^{5} + 5 x^{4} - 10 x^{2} + 6$ term by term:

   1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$

   2. 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: $20 x^{3}$

   3. The derivative of a constant times a function is the constant times the derivative of the function.

      1. 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: $20 x$

      So, the result is: $- 20 x$

   4. The derivative of the constant $6$ is zero.

   The result is: $5 x^{4} + 20 x^{3} - 20 x$

2. Now simplify:

   $$5 x \left(x^{3} + 4 x^{2} - 4\right)$$

The answer is:

$$5 x \left(x^{3} + 4 x^{2} - 4\right)$$