Derivative of y=x^3/3-4x^2+7x-8

1. Differentiate $\left(7 x + \left(\frac{x^{3}}{3} - 4 x^{2}\right)\right) - 8$ term by term:

   1. Differentiate $7 x + \left(\frac{x^{3}}{3} - 4 x^{2}\right)$ term by term:

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

         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: $x^{2} - 8 x$

      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: $7$

      The result is: $x^{2} - 8 x + 7$

   2. The derivative of the constant $-8$ is zero.

   The result is: $x^{2} - 8 x + 7$

The answer is:

$$x^{2} - 8 x + 7$$