AP Calculus BC / Unit 2: Differentiation: Definition and Fundamental Properties
2.9 The Quotient Rule
Notes
$$\frac{d}{dx}\frac{f}{g}=\frac{f'g-fg'}{g^2}$$
- Memory aid: "low d-high minus high d-low, over low squared."
Practice
$\displaystyle \frac{d}{dx}\frac{x}{x+1}=$
$\displaystyle \frac{(x+1)-x}{(x+1)^2}$.
$f(1)=2$, $f'(1)=3$, $g(1)=4$, $g'(1)=1$. Find $\displaystyle \left(\frac{f}{g}\right)'(1)$.
$\displaystyle \frac{3(4)-2(1)}{16}=\frac{10}{16}=\frac{5}{8}$.
In the quotient rule, the order of the numerator terms:
Swapping them flips the sign.
Ready for more? Take the Unit 2 test.