Derivative of x^3-1/5*x^2+2*x-4

1. Differentiate $\left(2 x + \left(x^{3} - \frac{x^{2}}{5}\right)\right) - 4$ term by term:

   1. Differentiate $2 x + \left(x^{3} - \frac{x^{2}}{5}\right)$ term by term:

      1. Differentiate $x^{3} - \frac{x^{2}}{5}$ 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: $- \frac{2 x}{5}$

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

      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: $2$

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

   2. The derivative of the constant $-4$ is zero.

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

The answer is:

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