Derivative of cosx-x^9

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

   1. The derivative of cosine is negative sine:

      $$\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$$

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

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

      So, the result is: $- 9 x^{8}$

   The result is: $- 9 x^{8} - \sin{\left(x \right)}$

The answer is:

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