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

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

   1. Differentiate $8 x^{5} + 3 x$ 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: $x^{5}$ goes to $5 x^{4}$

         So, the result is: $40 x^{4}$

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

         1. Apply the power rule: $x$ goes to $1$

         So, the result is: $3$

      The result is: $40 x^{4} + 3$

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

   The result is: $40 x^{4} + 3$

The answer is:

$$40 x^{4} + 3$$