Exercises for Question Type 6: Learning to apply the quotient rule on all derivatives in fraction form

Question 1

Skill question

Differentiate $f (x) = \frac{3 x ^{2} + 5 x - 2}{2 x ^{3} - x}$

[5]

Question 2

Skill question

Differentiate $f (x) = \frac{x ^{2} - 4}{x ^{3} + 1}$

[3]

Question 3

Skill question

Differentiate $f (x) = \frac{x + ln x}{x ^{2} + 1}$ [4 marks]

[4]

Question 4

Skill question

Differentiate $f (x) = \frac{s i n ( x )}{1 + c o s ( x )}$

[4]

Question 5

Skill question

Differentiate $f (x) = \frac{a r c t a n ( x ) + x ^{2}}{x ^{3}}$ [5 marks]

[5]

Question 6

Skill question

Differentiate $f (x) = \frac{x ^{3} - 3 x}{s i n ( x )}$

[3]

Question 7

Skill question

Differentiate $f (x) = \frac{s i n ( x ) + l n ( x )}{3 x ^{2}}$

[4]

Question 8

Skill question

Differentiate $f (x) = \frac{x e ^{x}}{x + 2}$

[4]

Question 9

Skill question

Differentiate $f (x) = \frac{2 x + 1}{x ^{2}}$ [3 marks]

[3]

Question 10

Skill question

Differentiate $f (x) = \frac{e ^{x} + x}{x - 1}$

[4]

Question 11

Skill question

Differentiate $f (x) = \frac{l n ( x ) + 1}{x ^{2} - x}$

[3]

Question 12

Skill question

Differentiate $f (x) = \frac{( x ^{2} + 1 ) e ^{x}}{x}$

[5]

IB Mathematics Analysis and Approaches Question Type 6: Learning to Apply the Quotient Rule on All Derivatives in Fraction Form Exercises