Exercises for Question Type 1: Calculating second derivatives of functions

Question 1

Skill question

Find the second derivative $f^{''} (x)$ for $f (x) = 3 e^{2 x}$ .

[2]

Question 2

Skill question

Find the second derivative $f^{''} (x)$ for the function $f (x) = \frac{cos ( ln x ) e ^{- x}}{x ln x}$

[9]

Question 3

Skill question

The objective of this question is to demonstrate the process of finding the second derivative of a polynomial function using the power rule.

Find the second derivative $f^{''} (x)$ if $f (x) = x^{4}$ .

[2]

Question 4

Skill question

Find the second derivative $f^{''} (x)$ for the function $f (x) = ln (sin x)$ .

[3]

Question 5

Skill question

Find the second derivative $f^{''} (x)$ for the function $f (x) = sin (ln (x^{2} + 1))$ .

[6]

Question 6

Skill question

Find the second derivative $f^{''} (x)$ for $f (x) = ln (x)$ .

[2]

Question 7

Skill question

Find the second derivative $f^{''} (x)$ for $f (x) = ln (x^{2} + 1)$ .

[4]

Question 8

Skill question

Derivatives of inverse circular functions, including the chain rule and quotient rule.

Find the second derivative $f^{''} (x)$ for $f (x) = tan^{- 1} (x^{2})$ .

[4]

Question 9

Skill question

Find the second derivative $f^{''} (x)$ for $f (x) = x^{2} e^{x}$ .

[4]

Question 10

Skill question

Find the second derivative $f^{''} (x)$ for $f (x) = e^{- x} cos x$ .

[5]

Question 11

Skill question

Find the second derivative $f^{''} (x)$ for $f (x) = sin (ln x)$ .

[5]

Question 12

Skill question

Find the second derivative $f^{''} (x)$ for $f (x) = \frac{s i n x}{x}$ .

[6]

IB Mathematics Applications & Interpretation Question Type 1: Calculating Second Derivatives of Functions Exercises