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?)
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