0606.14.3: Know and use the derivatives of the standard Includes constant multiples, sums and comp…: past paper questions

Real questions on 0606.14.3: know and use the derivatives of the standard includes constant multiples, sums and comp…

The newest 20 of 71 written questions. Open one to see it on the real paper.

1. 0606/11 · May/June 2026 · Q7a[5]
   A curve has equation $y=\frac{4+{\mathrm{e}}^{2x}}{2+{\mathrm{e}}^x}$. (a) Show that, when $\frac{\mathrm{d}y}{\mathrm{d}x}=0$, ${\mathrm{e}}^{2x}+4{\mathrm{e}}^x-4=0$.See it on the paper →
2. 0606/21 · May/June 2026 · Q5a[4]
   It is given that $y={\tan }^{3}5x$. (a) Find $\frac{dy}{dx}$ in terms of $\tan 5x$.See it on the paper →
3. 0606/21 · May/June 2026 · Q5b[5]
   It is given that $y={\tan }^{3}5x$. (b) Hence solve the equation $\frac{\mathrm{d}y}{\mathrm{d}x}=0$ for $0⩽x<\frac{4\pi }{5}$.See it on the paper →
4. 0606/22 · May/June 2026 · Q3a[3]
   Differentiate $y=\sqrt{x+1}+\cos (5x+3)$ with respect to $x$.See it on the paper →
5. 0606/22 · May/June 2026 · Q9b[2]
   A particle $P$ moves in a straight line such that $t$ seconds after passing through a fixed point $O$, its displacement from $O$, $s$ metres, is given by $s={\mathrm{e}}^{4t}-10{\mathrm{e}}^{2t}+9$. (b) Find the acceleration of $P$ when $t=\ln 2$.See it on the paper →
6. 0606/12 · February/March 2026 · Q7[4]
   7 The variables $x$ and $y$ are related by $y=3\sqrt{x}+\frac{1}{\sqrt{x}}$. Use calculus to find the approximate change in $y$ when $x$ increases from $4$ to $4+h$, where $h$ is small.See it on the paper →
7. 0606/12 · February/March 2026 · Q8a[3]
   8 A curve has equation $y=x{e}^{2x+1}$. (a) Find $\frac{dy}{dx}$.See it on the paper →
8. 0606/02 · Specimen 2025 · Q5[3]

   3-mark question — its maths and diagrams are best seen on the paper.

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9. 0606/02 · Specimen 2025 · Q6[7]

   7-mark question — its maths and diagrams are best seen on the paper.

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10. 0606/11 · October/November 2025 · Q7a[4]
    Differentiate $\frac{\sin x+\cos x}{e^{1-3x}}$ with respect to $x$.See it on the paper →
11. 0606/21 · October/November 2025 · Q8a(i)[3]
    In this question, the units are metres and seconds. A particle $P$ is travelling in a straight line through a fixed point $O$. At time $t$ its acceleration, $a$, is given by $a=(2t-3{)}^2$, where $t\ge 0$. When $t=3$, $P$ has a velocity of 6. (a) (i) Find an expression for the velocity, $v$, of $P$ at time $t$.See it on the paper →
12. 0606/21 · October/November 2025 · Q8a(ii)[3]
    In this question, the units are metres and seconds. A particle $P$ is travelling in a straight line through a fixed point $O$. At time $t$ its acceleration, $a$, is given by $a=(2t-3{)}^2$, where $t\ge 0$. When $t=3$, $P$ has a velocity of 6. (ii) Find the time when $P$ is at rest.See it on the paper →
13. 0606/22 · May/June 2025 · Q2b[2]

    2-mark “Give” question — its maths and diagrams are best seen on the paper.

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14. 0606/22 · May/June 2025 · Q2d[1]

    1-mark “Find” question — its maths and diagrams are best seen on the paper.

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15. 0606/22 · May/June 2025 · Q4a[4]
    (a) Given that $y=4\sin 2x\cos 2x$, find the value of $\frac{\mathrm{d}y}{\mathrm{d}x}$ when $x=\frac{\pi }{6}$.See it on the paper →
16. 0606/23 · May/June 2025 · Q8a[3]
    It is given that $y={\mathrm{e}}^{3x+2}\tan x$. Use calculus to find the approximate change in $y$ as $x$ increases from $0.1$ to $0.1+h$, where $h$ is small.See it on the paper →
17. 0606/12 · February/March 2025 · Q12a[3]
    12 It is given that $y=x{\mathrm{e}}^{3x+2}$. (a) Find $\frac{\mathrm{d}y}{\mathrm{d}x}$.See it on the paper →
18. 0606/22 · October/November 2024 · Q2a[3]

    3-mark “Find” question — its maths and diagrams are best seen on the paper.

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19. 0606/23 · October/November 2024 · Q12c[1]
    12 A particle moves in a straight line. Its velocity, $v{\text{ ms}}^{-1}$, at time $t$ seconds is given by $v=\cos t-\sin t$. (c) Find an expression for $a$ in terms of $s$.See it on the paper →
20. 0606/12 · May/June 2024 · Q3[4]

    4-mark “Given” question — its maths and diagrams are best seen on the paper.

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What examiners said

Comprehensive responses • Very many candidates stated a fully correct derivative. Limited responses • Some responses could be improved by ensuring the use :wof product rule or to differentiate e2x + 1 as (2x + 1)e2x + 1 .

— Examiner report, February/March 2026, 0606/12 Q8(a) (Cambridge)

Some candidates offered fully correct answers, in a factorised form, as required. As the expression for the velocity was quadratic, the factorised form needed to be a product of simple linear factors. In the best responses, candidates gave the answer 3(t – 2)(t – 4). There were two approaches to answering this part of the question. In the more common approach, candidates multiplied out (t – 4)2(...

— Examiner report, May/June 2025, 0606/22 Q2(b) (Cambridge)

A good proportion of candidates earned the mark for correctly differentiating their 3-term quadratic expression for v. Some candidates used the product rule again. Some of these did not simplify their answers to part (b), resulting in a lot of work in this part, and increasingly the likelihood of errors. A few candidates stated a correct expression for a, then divided through by 6. In the weakest...

— Examiner report, May/June 2025, 0606/22 Q2(d) (Cambridge)