Exercises for Question Type 4: Deriving functions with a combination of product and chain rule

Question 1

Skill question

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

[4]

Question 2

Skill question

Calculus: Differentiation

Find the derivative of $f (x) = (ln x)^{3} sin (x^{2})$ .

[6]

Question 3

Skill question

Find $\frac{d}{d x} [e^{x^{2}} cos (x^{3})]$ .

[4]

Question 4

Skill question

Differentiate the function $f (x) = (3 x + 1)^{4} x^{2} + 2 x$ .

[6]

Question 5

Skill question

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

[4]

Question 6

Skill question

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

[5]

Question 7

Skill question

The function $f$ is defined by $f (x) = sin x ln x$ for $x \in (0, π)$ .

Find $f^{'} (x)$ .

[4]

Question 8

Skill question

Differentiate $f (x) = ln (5 x) x^{2} + 1$ .

[4]

Question 9

Skill question

Compute $\frac{d}{d x} [ln (sin (x^{2})) e^{x}]$ .

[4]

Question 10

Skill question

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

[3]

Question 11

Skill question

Differentiate $f (x) = e^{t a n x} x^{3}$ with respect to $x$ .

[4]

Question 12

Skill question

Compute the derivative of $f (x) = (x^{2} - 1)^{3} e^{2 x + 1}$ .

[5]

IB Mathematics Applications & Interpretation Question Type 4: Deriving Functions with a Combination of Product and Chain Rule Exercises