Exercises for Question Type 4: Learning to apply product rule on functions of x that are in multiple

Question 1

Skill question

Differentiate $y = (2 x + 1) (ln x) cos (3 x)$ with respect to $x$ (for $x > 0$ ). [5 marks]

[5]

Question 2

Skill question

Differentiate $y = e^{x} (ln x) cos x$ with respect to $x$ (for $x > 0$ ). [4]

Differentiate $y = e^{x} (ln x) cos x$ with respect to $x$ (for $x > 0$ ).

[4]

Question 3

Skill question

Differentiate $y = x^{3} (ln x) cos x$ with respect to $x$ (for $x > 0$ ).

[3]

Question 4

Skill question

Differentiate $f (x) = x^{2} e^{x} sin x$ with respect to $x$ . [4 marks]

[4]

Question 5

Skill question

Differentiate $y = x^{2} x ln x$ with respect to $x$ (for $x > 0$ ).

[4]

Question 6

Skill question

Differentiate $y = x (ln x) ln (2 x)$ with respect to $x$ (for $x > 0$ ).

[5]

Question 7

Skill question

Differentiate $y = 3 ln x sin x cos x$ with respect to $x$ (for $x > 0$ ).

[4]

Question 8

Skill question

Differentiate $y = x^{3} cos^{2} x$ with respect to $x$ .

[3]

Question 9

Skill question

Differentiate $y = (ln x)^{2} sin x cos x$ with respect to $x$ (for $x > 0$ ).

[5]

Question 10

Skill question

Differentiate $y = (ln x) (x sin x)$ with respect to $x$ (for $x > 0$ ).

[4]

Question 11

Skill question

Differentiate the following function with respect to $x$ .

Differentiate $y = x^{2} e^{2 x} ln x$ with respect to $x$ (for $x > 0$ ).

[5]

Question 12

Skill question

Differentiate $y = e^{x} (ln x) sin (2 x)$ with respect to $x$ (for $x > 0$ ).

[5]

Question 13

Skill question

Differentiate $y = (1 + x^{2}) (ln x) sin x$ with respect to $x$ (for $x > 0$ ).

[4]

IB Mathematics Analysis and Approaches Question Type 4: Learning to Apply Product Rule on Functions of x That Are in Multiple Exercises