Derivative of y=x⁵+2x³-x²+3

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

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

      1. Differentiate $x^{5} + 2 x^{3}$ 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: $x^{3}$ goes to $3 x^{2}$

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

         The result is: $5 x^{4} + 6 x^{2}$

      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: $5 x^{4} + 6 x^{2} - 2 x$

   2. The derivative of the constant $3$ is zero.

   The result is: $5 x^{4} + 6 x^{2} - 2 x$

2. Now simplify:

   $$x \left(5 x^{3} + 6 x - 2\right)$$

The answer is:

$$x \left(5 x^{3} + 6 x - 2\right)$$