Derivative of 6x^3+4x-7/3x-1

1. Differentiate $\left(- \frac{7 x}{3} + \left(6 x^{3} + 4 x\right)\right) - 1$ term by term:

   1. Differentiate $- \frac{7 x}{3} + \left(6 x^{3} + 4 x\right)$ term by term:

      1. Differentiate $6 x^{3} + 4 x$ 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: $x^{3}$ goes to $3 x^{2}$

            So, the result is: $18 x^{2}$

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

            1. Apply the power rule: $x$ goes to $1$

            So, the result is: $4$

         The result is: $18 x^{2} + 4$

      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: $- \frac{7}{3}$

      The result is: $18 x^{2} + \frac{5}{3}$

   2. The derivative of the constant $-1$ is zero.

   The result is: $18 x^{2} + \frac{5}{3}$

The answer is:

$$18 x^{2} + \frac{5}{3}$$