What is the difference between this two derivatives

Why I must use the quotient rule to find the derivative of $\dfrac{2}{x^2}$ and in the case of $\dfrac{x^3}{2} + \dfrac{3x}{2}$ I should use the product rule?

Answer

Hint:
$$\dfrac{2}{x^2}=2x^{-2}$$
and you can use the product rule.

More general:

The quotient rule for $\dfrac{f(x)}{g(x)}$ ghives the same result as the product rule for $f(x)[g(x)]^{-1}$ ( can you prove this result?)