Derivative of x^3-4x^2+3x

1. Differentiate $3 x + \left(x^{3} - 4 x^{2}\right)$ term by term:

   1. Differentiate $x^{3} - 4 x^{2}$ 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: $- 8 x$

      The result is: $3 x^{2} - 8 x$

   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: $3$

   The result is: $3 x^{2} - 8 x + 3$

The answer is:

$$3 x^{2} - 8 x + 3$$