Section 2.4: Reading questions on the product and quotient rules

Select all true statements about the derivatives of $f$ and $g$. There may be more than one correct answer.

A. $\displaystyle \left( f(x) g(x) \right)' = f'(x) g(x) + f(x) g'(x).$

B. $\displaystyle \left( \frac{f(x)}{g(x)} \right)' = \frac{g(x) f'(x) - f(x) g'(x)}{(g(x))^2}.$

C. $\displaystyle \left( f(x) g(x) \right)' = f'(x) g'(x).$

D. $\displaystyle \left( \frac{f(x)}{g(x)} \right)' = \frac{f'(x)}{g'(x)}.$

E. $\displaystyle \left( \frac{f(x)}{g(x)} \right)' = \frac{f(x) g'(x)-g(x) f'(x)}{(g'(x))^2}.$