Derivative of 3x^5-5x^3

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

      So, the result is: $- 15 x^{2}$

   The result is: $15 x^{4} - 15 x^{2}$

2. Now simplify:

   $$15 x^{2} \left(x^{2} - 1\right)$$

The answer is:

$$15 x^{2} \left(x^{2} - 1\right)$$