# Calculus - Differentiation - Quotient Rule

a - answer    s - solution    v - video    d - discussion

## Question 1

Use the quotient rule: when $y=\frac uv$, $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{u'v-v'u}{v^2}$ to differentiate the following:

a) $y=\frac{x+1}{x+2}$a s v d
b) $y=\frac{2x+1}{x+1}$a s v d
c) $y=\frac{2x-3}{4x+5}$a s v d
d) $y=\frac{4-x}{6x-10}$a s v d
e) $y=\frac{5x}{20x+11}$a s v d
f) $y=\frac{1-2x}{5x+6}$a s v d
g) $y=\frac{2x+5}{7-3x}$a s v d
h) $y=-\frac{33-2x}{5+2x}$a s v d
i) $y=\frac{ax+b}{a+bx}$a s v d

## Question 2

Use the quotient rule to differentiate the following:

a) $y=\frac{x^2+1}{x^2+2}$a s v d
b) $y=\frac{x^3-5}{x^2+6}$a s v d
c) $y=\frac{1-x^4}{2x+3}$a s v d
d) $y=\frac{3x^2-9}{2x^2+1}$a s v d
e) $y=\frac{6x^2+x}{2x-4}$a s v d
f) $y=\frac{4x^3-6x+1}{2x-3}$a s v d
g) $y=\frac{4x^2+6x+3}{x^2-5x+4}$a s v d

## Question 3

Use the quotient rule to differentiate the following:

a) $y=\frac{\sqrt{x}}{x+2}$a s v d
b) $y=\frac{\sqrt{x}+1}{\sqrt{x}-1}$a s v d
c) $y=\frac{\sqrt{x+5}}{2x+3}$a s v d
d) $y=\frac{\sqrt{x}-\sqrt3}{\sqrt{x-3}}$a s v d
e) $y=\frac{x{(x+2)}^2}{4x^3-8}$a s v d