Exercises for Question Type 5: Applying quotient rule on functions as a rational

Question 1

Skill question

Find the derivative of $\frac{[ l n ( x ) ] ^{2}}{x ^{3}}$ .

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Question 2

Skill question

Differentiate $\frac{e ^{- 2 x}}{x ^{2} + 3}$ with respect to $x$ .

[4]

Question 3

Skill question

Find the derivative of the function

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

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Question 4

Skill question

Differentiate $\frac{sin ( x ) + ln ( x )}{3 x ^{2}}$ with respect to $x$ .

[5]

Question 5

Skill question

The question requires the application of the quotient rule, product rule, and chain rule to find the derivative of a complex transcendental function.

Find $\frac{d}{d x} [\frac{cos ( ln x ) e ^{- x}}{x ln x}]$ .

[5]

Question 6

Skill question

Differentiate $\frac{t a n ( x )}{x ^{2}}$ with respect to $x$ .

[3]

Question 7

Skill question

Differentiate $f (x) = \frac{l n ( x )}{x + 1}$ with respect to $x$ .

[5]

Question 8

Skill question

The question requires students to differentiate a rational function using the quotient rule and simplify the resulting expression.

Differentiate $\frac{x ^{2} + 1}{x - 1}$ with respect to $x$ .

[4]

Question 9

Skill question

Differential calculus

Find the derivative of $f (x) = \frac{e ^{x} + x ^{2}}{sin x}$ .

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Question 10

Skill question

Differentiate $\frac{s i n ^{2} ( x )}{l n ( x )}$ with respect to $x$ .

[3]

Question 11

Skill question

The question tests differentiation of a composite function requiring the use of the quotient, product, and chain rules. Students must identify the correct rule applications and simplify their final result through factorization.

Find $\frac{d}{d x} [\frac{x e ^{x^{2}}}{c o s x}]$ .

[5]

Question 12

Skill question

This question requires the application of differentiation rules, specifically the product and quotient rules.

Compute $\frac{d}{d x} [\frac{x ^{3} cos ( x )}{1 + x ^{2}}]$ .

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IB Mathematics Applications & Interpretation Question Type 5: Applying Quotient Rule on Functions as a Rational Exercises