Exercises for Question Type 3: Higher-order derivatives of functions with repeating patterns

Question 1

Skill question

Find $f^{(4)} (x)$ for $f (x) = e^{3 x}$ .

[2]

Question 2

Skill question

Evaluate $h^{(5)} (\frac{π}{4})$ for $h (x) = sin x - cos x$ . [4 marks]

[4]

Question 3

Skill question

Compute $y^{(5)} (x)$ for $y = sin (2 x)$ .

[3]

Question 4

Skill question

Find the sixth derivative of $y = cos (5 x)$ .

[3]

Question 5

Skill question

Evaluate $f^{(6)} (0)$ for $f (x) = sin (3 x)$ .

[3]

Question 6

Skill question

Find the smallest positive integer $n$ such that $f^{(n)} (x) = f (x)$ for $f (x) = sin x + cos x$ .

[3]

Question 7

Skill question

Evaluate $f^{(5)} (0)$ for $f (x) = cos (2 x) + sin (3 x)$ .

[4]

Question 8

Skill question

Find $y^{(6)} (x)$ for $y = sin x + 2 sin (x + \frac{π}{3})$ .

[4]

IB Mathematics Analysis and Approaches Question Type 3: Higher-order Derivatives of Functions with Repeating Patterns Exercises