Derivative of 2/5x^5-sqrt(3)x^2-7

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

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

         So, the result is: $2 x^{4}$

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

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

         So, the result is: $- 2 \sqrt{3} x$

      The result is: $2 x^{4} - 2 \sqrt{3} x$

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

   The result is: $2 x^{4} - 2 \sqrt{3} x$

2. Now simplify:

   $$2 x \left(x^{3} - \sqrt{3}\right)$$

The answer is:

$$2 x \left(x^{3} - \sqrt{3}\right)$$