Derivative of y=7x^6-6x-8

1. Differentiate $\left(7 x^{6} - 6 x\right) - 8$ term by term:

   1. Differentiate $7 x^{6} - 6 x$ 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: $x^{6}$ goes to $6 x^{5}$

         So, the result is: $42 x^{5}$

      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: $-6$

      The result is: $42 x^{5} - 6$

   2. The derivative of the constant $-8$ is zero.

   The result is: $42 x^{5} - 6$

The answer is:

$$42 x^{5} - 6$$