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Mathematics - Differentiation

Practise 74 JEE Main previous year questions on Differentiation, compiled from papers spanning 2002 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 JEE Main tests.

Differentiation has been asked in 20 of the 25 years of JEE Main papers analysed (2002–2026), with 74 questions in all. 16% of them were easy, 53% moderate and 31% tough. Most of its questions came from 2024, with 11 questions that year. In the last three years (2024–2026) it had 13 questions across 49 papers, about 0.3 per paper.

The chapter's 9 topics are not weighted equally: Differentiation of composite functions (26 questions, 35%), Higher order derivatives (13 questions, 18%), and Differentiation of implicit functions (8 questions, 11%) have been asked the most. Over the last five years the most frequent topics have been Higher order derivatives (9), Differentiation of composite functions (7), and Functional Equation (7). Differentiation of composite functions has produced the most tough questions (11).

  1. 1Let and be twice differentiable functions satisfying for all , and . Then is equal to :05 Apr, 2026 (E)Functional Equation
  2. 2Let be a real polynomial of degree such that , for all . If , then is equal to:04 Apr, 2026 (M)Functional Equation
  3. 3Let . Then the value of is:21 Jan, 2026 (E)Functional Equation
  4. 4Let be a twice differentiable function such that , for all . If , then the value of is:02 Apr, 2025 (M)Functional Equation
  5. 5Let be such that and . Then is equal to:09 Apr, 2024 (M)Functional Equation
  6. 6If , then at is equal to09 Apr, 2024 (E)Differentiation of composite functions
  7. 7If then06 Apr, 2024 (M)Differentiation of composite functions
  8. 8Suppose for a differentiable function and . If , then is equal to:06 Apr, 2024 (E)Differentiation of composite functions
  9. 9If , then at is equal to :05 Apr, 2024 (E)Higher order derivatives
  10. 10Let for all . Consider a function such that for all . Then the value of is :04 Apr, 2024 (M)Differentiation of composite functions
  11. 11If y = x + 1 x 2 − x x x + x + x + 1 15 3 cos 2 x − 5 cos 3 x , then 96 y ' π 6 is equal to:01 Feb, 2024 (E)Higher order derivatives
  12. 12Suppose f x = 2 x + 2 - x tan x tan - 1 x 2 - x + 1 7 x 2 + 3 x + 1 3 . Then the value of f ' 0 is equal to29 Jan, 2024 (M)Differentiation of composite functions
  13. 13Let y = log e 1 - x 2 1 + x 2 , - 1 x 1 . Then at x = 1 2 , the value of 225 y ' - y " is equal to29 Jan, 2024 (E)Higher order derivatives
  14. 14Let f ( x ) = x 3 + x 2 f ' ( 1 ) + x f " ( 2 ) + f ''' ( 3 ) , x ∈ R . Then f ' ( 10 ) is equal to27 Jan, 2024 (M)Functional Equation
  15. 15Let for a differentiable function f : ( 0 , ∞ ) → R , f x - f y ≥ log e x y + x - y , ∀ x , y ∈ 0 , ∞ . Then ∑ n = 1 20 f ' 1 n 2 is equal t27 Jan, 2024 (M)Differentiation of composite functions
  16. 16Let f x = sin x + cos - 2 sin x - cos x , x 0 , - 4 , then f 7 12 f 7 12 is equal to08 Apr, 2023 (M)Higher order derivatives
  17. 17If 2 x y + 3 y x = 20 , then d y d x at 2 , 2 is equal to:06 Apr, 2023 (M)Logarithmic differentiation
  18. 18If y x = x x , x 0 , then y 2 - 2 y 2 is equal to :01 Feb, 2023 (E)Higher order derivatives
  19. 19Let y = f x = sin 3 3 cos 3 2 - 4 x 3 + 5 x 2 + 1 3 2 . Then, at x = 1 ,31 Jan, 2023 (M)Differentiation of composite functions
  20. 20Let y x = 1 + x 1 + x 2 1 + x 4 1 + x 8 1 + x 16 . Then y - y at x = - 1 is equal to25 Jan, 2023 (M)Higher order derivatives
  21. 21Let x t = 2 2 cos t sin 2 t and y t = 2 2 sin t sin 2 t , t 0 , 2 . Then 1 + d y d x 2 d 2 y dx 2 at t = 4 is equal to28 Jul, 2022 (E)Parametric differentiation
  22. 22For the curve C : x 2 + y 2 - 3 + x 2 - y 2 - 1 5 = 0 , the value of 3 y - y 3 y , at the point , , 0 , on C , is equal to ________.27 Jul, 2022 (E)Higher order derivatives
  23. 23The value of log e 2 d dx log cos x cosec x at x = 4 is26 Jul, 2022 (E)Logarithmic differentiation
  24. 24If cos - 1 y 2 = log e x 5 5 , y 2 , then27 Jun, 2022 (M)Higher order derivatives
  25. 25If y x = x x x , x 0 then d 2 x d y 2 + 20 at x = 1 is equal to27 Jun, 2022 (E)Logarithmic differentiation
  26. 26Let f : satisfy f x + y = 2 x f y + 4 y ( f x , x , y . If f 2 = 3 , then 14 f 4 f 2 is equal to _____.26 Jun, 2022 (E)Functional Equation
  27. 27Let f : R R be defined as f x = x 3 + x - 5 . If g x is a function such that f g x = x , x R , then g 63 is equal to ______25 Jun, 2022 (M)Derivative of function and its inverse
  28. 28If y = tan - 1 sec x 3 - tan x 3 , 2 x 3 3 2 , then24 Jun, 2022 (E)Higher order derivatives
  29. 29If y 1 / 4 + y - 1 / 4 = 2 x , and x 2 - 1 d 2 y d x 2 + x d y d x + y = 0 , then | - | is equal to _______.27 Aug, 2021 (M)Higher order derivatives
  30. 30If y ( x ) = cot - 1 1 + sin x + 1 - sin x 1 + sin x - 1 - sin x , x 2 , , then d y d x at x = 5 6 is:27 Aug, 2021 (E)Differentiation of Inverse Trigonometric Functions
  31. 31Let f ( x ) = cos 2 tan - 1 sin cot - 1 1 - x x , 0 x 1 . Then:26 Aug, 2021 (M)Differentiation of Inverse Trigonometric Functions
  32. 32If y = y ( x ) is an implicit function of x such that log e ( x + y ) = 4 x y , then d 2 y d x 2 at x = 0 is equal to26 Aug, 2021 (M)Differentiation of implicit functions
  33. 33If f x = sin cos - 1 1 - 2 2 x 1 + 2 2 x and its first derivative with respect to x is - b a log e 2 when x = 1 , where a and b are integers17 Mar, 2021 (M)Differentiation of Inverse Trigonometric Functions
  34. 34Let f : S S where S = 0 , be a twice differentiable function such that f x + 1 = x f x . If g : S R be defined as g x = log e f x , then the16 Mar, 2021 (E)Higher order derivatives
  35. 35The derivative of tan - 1 1 + x 2 - 1 x with respect to tan - 1 2 x 1 - x 2 1 - 2 x 2 at x = 1 2 is :05 Sep, 2020 (E)Derivative of f(x) wrt g(x)
  36. 36If a + 2 b cos x ) ( a - 2 b cos y = a 2 - b 2 , where a b 0 , then d x d y at 4 , 4 is:04 Sep, 2020 (M)Differentiation of implicit functions
  37. 37If y 2 + log e cos 2 x = y , x - 2 , 2 then :03 Sep, 2020 (M)Differentiation of composite functions
  38. 38Let f be any function continuous on a , b and twice differentiable on a , b . If all x a , b , f x 0 and f x 0 , then for any c a , b , f c 09 Jan, 2020 (M)Differentiation of composite functions
  39. 39If x = 2 sin - sin 2 and y = 2 cos - cos 2 , 0 , 2 , then d 2 y d x 2 at = is:09 Jan, 2020 (E)Parametric differentiation
  40. 40Let f and g be differentiable functions on R such that f o g is the identity function. If for some a , b R , g a = 5 and g a = b , then f b 09 Jan, 2020 (E)Derivative of function and its inverse
  41. 41Let f x = sin tan - 1 x + sin cot - 1 x 2 - 1 , x 1 . If d y d x = 1 2 d d x sin - 1 f x and y 3 = 6 , then y - 3 is equal to:08 Jan, 2020 (M)Differentiation of Inverse Trigonometric Functions
  42. 42If y = 2 t a n + c o t 1 + t a n 2 + 1 s i n 2 , 3 4 , , then d y d at = 5 6 is07 Jan, 2020 (M)Differentiation of composite functions
  43. 43Let x k + y k = a k , a , k 0 and d y d x + y x 1 3 = 0 , then k is07 Jan, 2020 (M)Differentiation of implicit functions
  44. 44Let y = y x be a function of x satisfying y 1 - x 2 = k - x 1 - y 2 where k is a constant and y 1 2 = - 1 4 .Then d y d x at x = 1 2 , is eq07 Jan, 2020 (E)Differentiation of implicit functions
  45. 45If e y + x y = e , the ordered pair d y d x , d 2 y d x 2 at x = 0 is equal to12 Apr, 2019 (M)Differentiation of implicit functions
  46. 46The derivative of t a n - 1 s i n x - c o s x s i n x + c o s x with respect to x 2 , where x 0 , 2 , is12 Apr, 2019 (E)Derivative of f(x) wrt g(x)
  47. 47If 2 y = cot - 1 3 cos x + sin x cos x - 3 sin x 2 x 0 , 2 , then d y d x is equal to08 Apr, 2019 (M)Differentiation of Inverse Trigonometric Functions
  48. 48If f 1 = 1 , f 1 = 3 , then the derivative of f f f x + f x 2 at x = 1 is:08 Apr, 2019 (E)Differentiation of composite functions
  49. 49For x 1 , if 2 x 2 y = 4 e 2 x - 2 y , then 1 + log e 2 x 2 d y d x is equal to12 Jan, 2019 (M)Logarithmic differentiation
  50. 50Let f be a differentiable function such that f 1 = 2 and f ' x = f x for all x R . If h x = f f x , then h ' 1 is equal to :12 Jan, 2019 (E)Differentiation of composite functions

Frequently Asked Questions

1.How many questions are available for Differentiation?

This chapter includes 74 questions compiled from JEE Main papers spanning 2002 to 2026.

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

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

3.Is Differentiation an important chapter for JEE Main Mathematics?

Differentiation has appeared in 20 of the 25 years of JEE Main papers covered here, with 74 questions across 70 papers - about one per paper it appears in.

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

Of the 74 questions analysed for this chapter, 16% are easy, 53% moderate and 31% tough. 2024 had the most, with 11 questions.

5.Which topics in Differentiation should I focus on?

These topics have carried the most weightage in Differentiation:

  • Differentiation of composite functions - 26 questions (35%)
  • Higher order derivatives - 13 questions (18%)
  • Differentiation of implicit functions - 8 questions (11%)
  • Differentiation of composite functions has produced the most tough questions (11).
6.Is Differentiation's weightage in JEE Main going up or down?

Across all 70 papers analysed, Differentiation has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.