Derivative of x^3+6x^2+9x

1. Differentiate $9 x + \left(x^{3} + 6 x^{2}\right)$ term by term:

   1. Differentiate $x^{3} + 6 x^{2}$ 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. Apply the power rule: $x^{2}$ goes to $2 x$

         So, the result is: $12 x$

      The result is: $3 x^{2} + 12 x$

   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: $9$

   The result is: $3 x^{2} + 12 x + 9$

The answer is:

$$3 x^{2} + 12 x + 9$$