Exercises for Question Type 3: Applying product rule on multiplying functions

Question 1

Skill question

Differentiate $f (x) = ln (x^{2} + 1) sin (x^{3})$

[5]

Question 2

Skill question

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

[5]

Question 3

Skill question

Differentiate $f (x) = x e^{x} sin (x)$

[3]

Question 4

Skill question

Differentiate $f (x) = sin (e^{x} + x^{2}) ln (x^{2} + 1)$ .

[6]

Question 5

Skill question

Calculus: Differentiation using product or quotient rules.

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

[3]

Question 6

Skill question

Differentiate $f (x) = ln (x) sec (x)$ .

[3]

Question 7

Skill question

The following question requires the application of the product rule for multiple functions.

Differentiate $f (x) = 3 ln (x) sin (x) cos (x)$

[4]

Question 8

Skill question

This question requires the application of the product rule and knowledge of the derivative of the inverse tangent function.

Differentiate $f (x) = (x^{2} + 1) arctan (x)$ .

[4]

Question 9

Skill question

Differentiation of functions using the product rule and chain rule.

Differentiate $f (x) = e^{3 x} cos (2 x)$ .

[5]

Question 10

Skill question

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

[3]

Question 11

Skill question

Differentiate $f (x) = (x^{3} + 1) x ln (x)$

[4]

Question 12

Skill question

Calculus: Differentiation using product and chain rules.

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

[5]

IB Mathematics Applications & Interpretation Question Type 3: Applying Product Rule on Multiplying Functions Exercises