Derivative of x^3-9x^2

1. Differentiate $x^{3} - 9 x^{2}$ term by term:

   1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

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

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

         1. Apply the power rule: $x^{2}$ goes to $2 x$

         So, the result is: $18 x$

      So, the result is: $- 18 x$

   The result is: $3 x^{2} - 18 x$

2. Now simplify:

   $$3 x \left(x - 6\right)$$

The answer is:

$$3 x \left(x - 6\right)$$