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Mathematics - Differentiation

Practise 104 NDA previous year questions on Differentiation, compiled from papers spanning 2010 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NDA tests.

Differentiation has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 104 questions in all. 13% of them were easy, 81% moderate and 7% tough. Most of its questions came from 2015, with 10 questions that year. In the last three years (2024–2026) it had 14 questions across 5 papers, about 2.8 per paper.

The chapter's 7 topics are not weighted equally: Differentiation of composite functions (63 questions, 61%), Higher order derivatives (14 questions, 13%), and Differentiation of implicit functions (13 questions, 13%) have been asked the most. Differentiation of composite functions has also led over the last five years, with 21 questions. Differentiation of composite functions has produced the most tough questions (4).

  1. 1If , then what is equal to ?2026 (Phase 1)Differentiation of composite functions
  2. 2Passage: Let , where is a function of whose domain is . Question: What is equal to ?2026 (Phase 1)Differentiation of implicit functions
  3. 3Passage: Let , where is a function of whose domain is . Question: What is equal to, given that when ?2026 (Phase 1)Differentiation of implicit functions
  4. 4Consider the following for the two (02) items that follow: Let and . What is equal to?2025 (Phase 1)Differentiation of composite functions
  5. 5Consider the following for the two (02) items that follow: Let and . What is equal to?2025 (Phase 1)Differentiation of composite functions
  6. 6Consider the following for the two (02) items that follow: Let , where , are positive integers. The derivative of with respect to2025 (Phase 1)Differentiation of implicit functions
  7. 7Consider the following for the two (02) items that follow: Let , where , are positive integers. If , then what is equal to?2025 (Phase 1)Differentiation of implicit functions
  8. 8Consider the following for the two (02) items that follow: Let . What is equal to?2025 (Phase 1)Differentiation of Inverse Trigonometric Functions
  9. 9For the following three (03) items: Let . What is at equal to?2025 (Phase 2)Differentiation of composite functions
  10. 10For the following three (03) items: Let . If , then what is equal to?2025 (Phase 2)Parametric differentiation
  11. 11For the following two (02) items: Consider the function f'(-1)$ equal to?2025 (Phase 2)Differentiation of composite functions
  12. 12Let and be two functions such that and o . What is equal to?2024 (Phase 1)Differentiation of composite functions
  13. 13Paragraph: Let be a differentiable function with and . Let and . Question: What is equal to?2024 (Phase 2)Differentiation of composite functions
  14. 14Paragraph: Let be a differentiable function with and . Let and . Question: What is equal to?2024 (Phase 2)Differentiation of composite functions
  15. 15Paragraph: Let Question: What is the derivative of at ?2023 (Phase 1)Differentiation of composite functions
  16. 16Paragraph: Let Question: What is the derivative of at ?2023 (Phase 1)Differentiation of composite functions
  17. 17Paragraph: Let Question: What is the derivative of , where ?2023 (Phase 1)Differentiation of composite functions
  18. 18What is the derivative of with respect to ?2023 (Phase 1)Differentiation of composite functions
  19. 19What is the derivative of ?2023 (Phase 1)Differentiation of composite functions
  20. 20Let a function f be defined on and If f is differentiable, then what is equal to?2023 (Phase 2)Differentiation of composite functions
  21. 21If where , then what is equal to?2023 (Phase 2)Differentiation of composite functions
  22. 22If and , then what is equal to?2023 (Phase 2)Differentiation of composite functions
  23. 23If , then what is at equal to?2022 (Phase 1)Differentiation of implicit functions
  24. 24If , then what is the value of at ?2022 (Phase 1)Differentiation of composite functions
  25. 25If , then what is equal to?2022 (Phase 2)Differentiation of composite functions
  26. 26If then which one of the following is correct?2022 (Phase 2)Differentiation of composite functions
  27. 27In , then what is at equal to?2022 (Phase 2)Differentiation of composite functions
  28. 28If , then which one of the following is correct?2022 (Phase 2)Differentiation of composite functions
  29. 29What is the derivative of with respect to at ?2021 (Phase 1)Differentiation of composite functions
  30. 30If and , then what is at equal to?2021 (Phase 1)Parametric differentiation
  31. 31What is the derivative of with respect to ?2021 (Phase 1)Differentiation of composite functions
  32. 32What is the derivative of with respect to ?2021 (Phase 2)Differentiation of composite functions
  33. 33If then what is at equal to?2021 (Phase 2)Differentiation of composite functions
  34. 34If , then what is at equal to?2021 (Phase 2)Differentiation of composite functions
  35. 35Let be a polynomial function such that . What is equal to?2021 (Phase 2)Differentiation of composite functions
  36. 36What is the derivative of with respect to ?2020Differentiation of Inverse Trigonometric Functions
  37. 37If , where is an arbitrary constant and is a function of , then what is equal to?2020Differentiation of implicit functions
  38. 38If , then what is equal to?2020Differentiation of implicit functions
  39. 39What is the derivative of with respect to ?2019 (Phase 1)Differentiation of composite functions
  40. 40If , then is equal to2019 (Phase 1)Differentiation of composite functions
  41. 41If , then2019 (Phase 1)Higher order derivatives
  42. 42Paragraph: Consider the equation Question: What is at equal to ?2019 (Phase 2)Differentiation of implicit functions
  43. 43Paragraph: Consider the equation Question: What is at equal to?2019 (Phase 2)Higher order derivatives
  44. 44Paragraph: Let and Question: If , then what is the derivative of ?2019 (Phase 2)Differentiation of composite functions
  45. 45What is the derivative of with respect to ?2019 (Phase 2)Differentiation of composite functions
  46. 46What is the derivative of the function2018 (Phase 1)Differentiation of composite functions
  47. 47If is an even function, where , then which one of the following is correct?2018 (Phase 1)Differentiation of composite functions
  48. 48If , then what is at equal to?2018 (Phase 1)Differentiation of composite functions
  49. 49If , then what is equal to?2018 (Phase 2)Differentiation of Inverse Trigonometric Functions
  50. 50If and , then what is equal to?2018 (Phase 2)Differentiation of composite functions

Frequently Asked Questions

1.How many questions are available for Differentiation?

This chapter includes 104 questions compiled from NDA papers spanning 2010 to 2026.

2.Are these questions only from NDA, or from other exams too?

These are NDA questions specifically for the Differentiation chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Differentiation an important chapter for NDA Mathematics?

Differentiation has appeared in 17 of the 17 years of NDA papers covered here, with 104 questions across 31 papers - about 3 per paper it appears in.

4.What is the difficulty level of Differentiation questions in NDA?

Of the 104 questions analysed for this chapter, 13% are easy, 81% moderate and 7% tough. 2015 had the most, with 10 questions.

5.Which topics in Differentiation should I focus on?

These topics have carried the most weightage in Differentiation:

  • Differentiation of composite functions - 63 questions (61%)
  • Higher order derivatives - 14 questions (13%)
  • Differentiation of implicit functions - 13 questions (13%)
  • Differentiation of composite functions has produced the most tough questions (4).
6.Is Differentiation's weightage in NDA going up or down?

Across all 31 papers analysed, Differentiation has averaged about 3.4 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.