Derivative of x^9-6*x^21-36

1. Differentiate $\left(- 6 x^{21} + x^{9}\right) - 36$ term by term:

   1. Differentiate $- 6 x^{21} + x^{9}$ term by term:

      1. Apply the power rule: $x^{9}$ goes to $9 x^{8}$

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

         1. Apply the power rule: $x^{21}$ goes to $21 x^{20}$

         So, the result is: $- 126 x^{20}$

      The result is: $- 126 x^{20} + 9 x^{8}$

   2. The derivative of the constant $-36$ is zero.

   The result is: $- 126 x^{20} + 9 x^{8}$

2. Now simplify:

   $$x^{8} \left(9 - 126 x^{12}\right)$$

The answer is:

$$x^{8} \left(9 - 126 x^{12}\right)$$