Derivative of f(x)=4x²-5x³+9x

1. Differentiate $- 5 x^{3} + 4 x^{2} + 9 x$ term by term:

   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: $8 x$

   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: $x^{3}$ goes to $3 x^{2}$

         So, the result is: $15 x^{2}$

      So, the result is: $- 15 x^{2}$

   3. 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: $- 15 x^{2} + 8 x + 9$

The answer is:

$$- 15 x^{2} + 8 x + 9$$