Derivative of y=8x^5+3x-5

1. Differentiate $8 x^{5} + 3 x - 5$ 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: $3$

   3. The derivative of the constant $\left(-1\right) 5$ is zero.

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

The answer is:

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