Derivative of 2x^8+8x^3-5

1. Differentiate $\left(2 x^{8} + 8 x^{3}\right) - 5$ term by term:

   1. Differentiate $2 x^{8} + 8 x^{3}$ term by term:

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

         1. Apply the power rule: $x^{8}$ goes to $8 x^{7}$

         So, the result is: $16 x^{7}$

      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: $24 x^{2}$

      The result is: $16 x^{7} + 24 x^{2}$

   2. The derivative of the constant $-5$ is zero.

   The result is: $16 x^{7} + 24 x^{2}$

2. Now simplify:

   $$x^{2} \left(16 x^{5} + 24\right)$$

The answer is:

$$x^{2} \left(16 x^{5} + 24\right)$$