Derivative of y=x^5-7x^3+2

1. Differentiate $\left(x^{5} - 7 x^{3}\right) + 2$ term by term:

   1. Differentiate $x^{5} - 7 x^{3}$ 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: $- 21 x^{2}$

      The result is: $5 x^{4} - 21 x^{2}$

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

   The result is: $5 x^{4} - 21 x^{2}$

2. Now simplify:

   $$x^{2} \left(5 x^{2} - 21\right)$$

The answer is:

$$x^{2} \left(5 x^{2} - 21\right)$$