Differentiation

89 NDA Mathematics previous year questions (PYQs) from 19 papers, 2017 to 2026, with answers and worked solutions.

About this chapter

Difficulty: 27 easy · 41 moderate · 21 hard.
Most-asked subtopics: Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions (51), Parametric, Implicit, and Higher-Order Derivatives (20), Differentiability of Absolute Value, Piecewise, and Greatest Integer Functions (18).
Updated 14 September 2026.

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NDA · Sep 2026 · Q91Easy
#1Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2026 · Q94Hard
#2Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2017 · Q89Moderate
#3Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2017 · Q95Easy
#4Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2017 · Q63Hard
#5Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2017 · Q65Easy
#6Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2017 · Q66Moderate
#7Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2017 · Q70Easy
#8Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2017 · Q73Moderate
#9Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2017 · Q82Moderate
#10Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2018 · Q87Moderate
#11Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2018 · Q97Easy
#12Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2018 · Q98Moderate
#13Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2018 · Q27Hard
#14Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2018 · Q71Moderate
#15Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2018 · Q76Easy
#16Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2018 · Q77Moderate
#17Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2018 · Q91Moderate
#18Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2018 · Q95Hard
#19Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2018 · Q98Hard
#20Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2019 · Q71Moderate
#21Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2019 · Q79Easy
#22Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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Set · 3 questions
Directions for the following three (03) items : Read the following information and answer the three items that follow : A curve $y = me^{mx}$ where $m > 0$ intersects $y$ -axis at a point $P$ .
- NDA · Sep 2019 · Q76Easy
  #23Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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- NDA · Sep 2019 · Q77Moderate
  #24Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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- NDA · Sep 2019 · Q78Easy
  #25Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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Set · 1 question
Directions for the following three (03) items : Read the following information and answer the three items that follow : Let $f(x) = x^{2} + 2x - 5$ and $g(x) = 5x + 30$ .
- NDA · Sep 2019 · Q93Easy
  #26Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2019 · Q97Moderate
#27Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2020 · Q94Easy
#28Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2021 · Q88Easy
#29Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2021 · Q91Moderate
#30Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2021 · Q71Moderate
#31Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2021 · Q72Moderate
#32Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2021 · Q80Moderate
#33Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2021 · Q94Easy
#34Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2022 · Q70Moderate
#35Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2022 · Q77Moderate
#36Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2022 · Q78Moderate
#37Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2022 · Q88Moderate
#38Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2022 · Q89Moderate
#39Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2022 · Q90Hard
#40Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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Set · 3 questions
Consider the following for the next three (03) items that follow: Let $f(x)=\begin{vmatrix}\cos x & x & 1\\2\sin x & x^{2} & 2x\\\tan x & x & 1\end{vmatrix}$ .
- NDA · Apr 2023 · Q76Easy
  #41Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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- NDA · Apr 2023 · Q77Hard
  #42Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
  Strategy Concept notes
- NDA · Apr 2023 · Q78Hard
  #43Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
  Strategy Concept notes
NDA · Apr 2023 · Q92Easy
#44Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Apr 2023 · Q94Moderate
#45Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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Set · 1 question
Let $f$ be defined on $\mathbb{R}\setminus\{0\}$ and $2f(x)+f\!\left(\frac{1}{x}\right)=x+3$ .
- NDA · Sep 2023 · Q44Moderate
  #46Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2023 · Q65Easy
#47Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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NDA · Sep 2023 · Q66Moderate
#48Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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Set · 2 questions
Let $f:(-1,1)\to\mathbb{R}$ be a differentiable function with $f(0)=-1$ and $f'(0)=1$ . Let $h(x)=f(2f(x)+2)$ and $g(x)=(h(x))^2$ .
- NDA · Sep 2024 · Q95Moderate
  #49Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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- NDA · Sep 2024 · Q96Moderate
  #50Differentiation Techniques — Chain Rule, Logarithmic, Composite Functions
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