Unit 5: Calculus

Topic 5.6: Differentiation Rules Questions

Practice 20 exam-style questions for IB Math AA SL Topic 5.6. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Find2 marks

2026

Differentiate y = (x² − 5)³.

Markscheme and model answer locked

Unlock Question

2Show that1 mark

2026

Show that

\frac{d y}{d x} = 10 (2 x + 1)^{4}

Markscheme and model answer locked

Unlock Question

3Choose1 mark

Differentiate

y = (2 x - 1) (x + 4)

without expanding the brackets first.

Markscheme and model answer locked

Unlock Question

4Find2 marks

2026

Differentiate y = (x + 3)(2x − 1) using the product rule.

Markscheme and model answer locked

Unlock Question

5Find2 marks

2026

Differentiate

y = (x^{2} - 5)^{3}

Markscheme and model answer locked

Unlock Question

6Choose1 mark

Use the product rule to differentiate

y = x^{2} (x + 5)

Markscheme and model answer locked

Unlock Question

7Find2 marks

2026

Differentiate

y = (4 x + 1)^{5}

Markscheme and model answer locked

Unlock Question

8Find2 marks

2026

Differentiate

y = (x + 3) (2 x - 1)

using the product rule.

Markscheme and model answer locked

Unlock Question

9Show that2 marks

2025

Let

f (x) = ln (3 + e^{2 x})

. Show that

f^{'} (x) = \frac{2 e ^{2 x}}{3 + e ^{2 x}}

Markscheme and model answer locked

Unlock Question

10Verify2 marks

2026

Verify that

y = 3 cos (2 t - 1)

satisfies

\frac{d ^{2} y}{d t ^{2}} = - 4 y

Markscheme and model answer locked

Unlock Question

11Choose1 mark

Differentiate

y = \frac{4 x}{x + 3}

with respect to

x

Markscheme and model answer locked

Unlock Question

12Find2 marks

2026

Differentiate y = (4x + 1)⁵.

Markscheme and model answer locked

Unlock Question

13Write down1 mark

2026

Write down

\frac{d y}{d x}

Markscheme and model answer locked

Unlock Question

14Find3 marks

2026

Differentiate

y = \frac{2 x + 1}{3 x - 1}

Markscheme and model answer locked

Unlock Question

15Find2 marks

2026

Differentiate

y = \frac{s i n x}{x}

Markscheme and model answer locked

Unlock Question

16Find3 marks

2026

Find the gradient of

y = x \cdot sin x

x = 0

Markscheme and model answer locked

Unlock Question

17Show that3 marks

2024

Let

y = x e^{2 x}

. Show that

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = 0

Markscheme and model answer locked

Unlock Question

18Find3 marks

2022

Let

f (x) = ln (x^{2} + 1)

. A differentiable function

g

has

g (1) = 2

and

g^{'} (1) = - 3

. Find

(f \circ g)^{'} (1)

Markscheme and model answer locked

Unlock Question

19Find2 marks

2026

Differentiate y = e^3x + cos(2x).

Markscheme and model answer locked

Unlock Question

20Find2 marks

2026

Differentiate y = sin(x²).

Markscheme and model answer locked

Unlock Question

Ready to practice Topic 5.6?

Get instant AI feedback on your answers, view detailed markschemes, and track your progress across all IB Math AA SL topics.

Start Practising Now Math AA SL Study Hub