Derivative of 3/2x^2-x^3

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

      So, the result is: $3 x$

   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: $- 3 x^{2}$

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

2. Now simplify:

   $$3 x \left(1 - x\right)$$

The answer is:

$$3 x \left(1 - x\right)$$