Leaving Cert Maths: Differentiation
How often Differentiation comes up on the Maths papers, every year it was asked, and questions to try.
HL Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
OL Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Quick ones on Differentiation.
- x⁵/5
- 4x³
- 4x⁴
- e³ˣ/3
- e³ˣ
- 3e³ˣ
- cos x
- −sin x
- −cos x
Show the answers
(a) 4x³
(b) 3e³ˣ
(c) cos x
Higher Level
Asked on 10 of the last 10 Higher Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Paper 1, Q3, Paper 1, Q7 |
| 2025 | Paper 1, Q2, Paper 1, Q3, Paper 1, Q8, Paper 1, Q9 |
| 2024 | Paper 1, Q3, Paper 1, Q4, Paper 1, Q5, Paper 1, Q7, Paper 1, Q8, Paper 1, Q9, Paper 1, Q10, Paper 2, Q8 |
| 2023 | Paper 1, Q2, Paper 1, Q5, Paper 1, Q7, Paper 1, Q9, Paper 1, Q10, Paper 2, Q7 |
| 2022 | Paper 1, Q5, Paper 1, Q6, Paper 1, Q7, Paper 1, Q10 |
| 2021 | Paper 1, Q5, Paper 1, Q6, Paper 1, Q8, Paper 1, Q9, Paper 1, Q10, Paper 2, Q9 |
| 2019 | Paper 1, Q8, Paper 1, Q9 |
| 2018 | Paper 1, Q3, Paper 1, Q7, Paper 1, Q8 |
| 2017 | Paper 1, Q3, Paper 1, Q5, Paper 1, Q7 |
| 2016 | Paper 1, Q6, Paper 1, Q7, Paper 1, Q8, Paper 2, Q8 |
Links open the State Examinations Commission’s paper for that year.
More Differentiation questions
Differentiation, 2 marks
d/dx (√x) = ?
- 2√x
- ½√x
- 1/(2√x)
Show the answer
1/(2√x)
Write √x as x^(1/2). Power rule: ½x^(−1/2) = 1/(2√x).
Differentiation, 2 marks
d/dx (7) = ?
- 7x
- 0
- 7
Show the answer
0
A constant never changes, so its rate of change (slope) is 0. The graph of y = 7 is a horizontal line.
Differentiation, 2 marks
Slope of y = eˣ at x = 0?
- 1
- 0
- e
Show the answer
1
dy/dx = eˣ, and at x = 0 that's e⁰ = 1.
Ordinary Level
Asked on 10 of the last 10 Ordinary Level papers, most recently in 2026. banker
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2026 | Q6, Q8 |
| 2025 | Q4, Q8 |
| 2024 | Q5, Q7 |
| 2023 | Q4, Q6 |
| 2022 | Q4, Q7, Q10 |
| 2021 | Q5 |
| 2019 | Q3, Q7 |
| 2018 | Q5, Q8 |
| 2017 | Q8 |
| 2016 | Q4, Q8 |
Links open the State Examinations Commission’s paper for that year.
More Differentiation questions
Differentiation, 2 marks
Differentiate y = x³.
- x⁴/4
- 3x³
- 3x²
Show the answer
3x²
Power rule: bring the power down in front and take 1 off the power, so x³ becomes 3x².
Differentiation, 2 marks
Differentiate y = 5x.
- 0
- 5
- 5x
Show the answer
5
y = 5x is a straight line with slope 5, so dy/dx = 5.
Differentiation, 2 marks
Differentiate y = x² + 3x.
- 2x + 3
- 2x + 3x
- x + 3
Show the answer
2x + 3
Differentiate term by term: x² gives 2x, and 3x gives 3. So dy/dx = 2x + 3.