Derivative of x^2-6x+4/3x-2

1. Differentiate $\left(\frac{4 x}{3} + \left(x^{2} - 6 x\right)\right) - 2$ term by term:

   1. Differentiate $\frac{4 x}{3} + \left(x^{2} - 6 x\right)$ term by term:

      1. Differentiate $x^{2} - 6 x$ term by term:

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

         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: $-6$

         The result is: $2 x - 6$

      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: $\frac{4}{3}$

      The result is: $2 x - \frac{14}{3}$

   2. The derivative of the constant $-2$ is zero.

   The result is: $2 x - \frac{14}{3}$

The answer is:

$$2 x - \frac{14}{3}$$