Derivative of y=x^6+5x^4+2x^3-x^2

1. Differentiate $- x^{2} + \left(2 x^{3} + \left(x^{6} + 5 x^{4}\right)\right)$ term by term:

   1. Differentiate $2 x^{3} + \left(x^{6} + 5 x^{4}\right)$ term by term:

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

         1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$

         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: $20 x^{3}$

         The result is: $6 x^{5} + 20 x^{3}$

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

         1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

         So, the result is: $6 x^{2}$

      The result is: $6 x^{5} + 20 x^{3} + 6 x^{2}$

   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: $- 2 x$

   The result is: $6 x^{5} + 20 x^{3} + 6 x^{2} - 2 x$

2. Now simplify:

   $$2 x \left(3 x^{4} + 10 x^{2} + 3 x - 1\right)$$

The answer is:

$$2 x \left(3 x^{4} + 10 x^{2} + 3 x - 1\right)$$