Derivative of 3x^5-2x^2

1. Differentiate $3 x^{5} - 2 x^{2}$ 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: $15 x^{4}$

   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: $- 4 x$

   The result is: $15 x^{4} - 4 x$

2. Now simplify:

   $$x \left(15 x^{3} - 4\right)$$

The answer is:

$$x \left(15 x^{3} - 4\right)$$