Derivative of 5x^4-2x^3+3/5x-7

1. Differentiate $\left(\frac{3 x}{5} + \left(5 x^{4} - 2 x^{3}\right)\right) - 7$ term by term:

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

      1. Differentiate $5 x^{4} - 2 x^{3}$ 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: $x^{4}$ goes to $4 x^{3}$

            So, the result is: $20 x^{3}$

         2. 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: $- 6 x^{2}$

         The result is: $20 x^{3} - 6 x^{2}$

      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: $\frac{3}{5}$

      The result is: $20 x^{3} - 6 x^{2} + \frac{3}{5}$

   2. The derivative of the constant $-7$ is zero.

   The result is: $20 x^{3} - 6 x^{2} + \frac{3}{5}$

The answer is:

$$20 x^{3} - 6 x^{2} + \frac{3}{5}$$