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Calculus - Differentiation - Quotient Rule

  a - answer    s - solution    v - video

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


Question 2


Use the quotient rule to differentiate the following:

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


Question 3


Use the quotient rule to differentiate the following:

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