Exercises for Question Type 2: Applying chain rule on composite functions

Exercises for Question Type 2: Applying chain rule on composite functions - IB

Written by official IB examiners

Question 1

Skill question

Calculus: Chain Rule

Find the derivative of

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

[3]

Question 2

Skill question

Candidates should be able to differentiate composite functions using the chain rule.

Compute the derivative of $f (x) = ln (sin x) .$

[2]

Question 3

Skill question

Calculus: Differentiation using the chain rule.

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

[2]

Question 4

Skill question

The student is required to find the derivative of a composite function involving the inverse tangent function, specifically $f (x) = arctan (3 x^{2} + 1)$ , using the chain rule.

Find the derivative of $f (x) = arctan (3 x^{2} + 1)$ .

[4]

Question 5

Skill question

Differentiate the function $f (x) = sin (ln x)$ where $x > 0$ .

[2]

Question 6

Skill question

Find $f^{'} (x)$ if $f (x) = e^{s i n (x^{2})} .$

[4]

Question 7

Skill question

Find the derivative of the function $f (x) = ln (x^{2} + 1) + sin (e^{3 x})$

[4]

Question 8

Skill question

Find $f^{'} (x)$ for $f (x) = 1 + e^{3 x} .$

[3]

Question 9

Skill question

Differentiation using the chain rule.

Find the derivative of $f (x) = (ln (x + 1))^{3}$ .

[3]

Question 10

Skill question

This question requires the application of the chain rule to differentiate a composite function involving an exponential function and a power.

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

[3]

Question 11

Skill question

Compute $f^{'} (x)$ if $f (x) = (cos (x^{2}))^{5} .$

[3]

Question 12

Skill question

The question requires the application of the chain rule to a composite function involving natural logarithms, trigonometric functions, and exponential functions.

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

[3]

IB Mathematics Applications & Interpretation Question Type 2: Applying Chain Rule on Composite Functions Exercises

IB Mathematics Applications & Interpretation Question Type 2: Applying Chain Rule on Composite Functions Exercises