Derivative of y=x^6-5x+7

1. Differentiate $\left(x^{6} - 5 x\right) + 7$ term by term:

   1. Differentiate $x^{6} - 5 x$ term by term:

      1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$

      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: $-5$

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

   2. The derivative of the constant $7$ is zero.

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

The answer is:

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