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Mathematics - Differentiation

Practise 46 NTA Abhyas (JEE Main) questions on Differentiation. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Differentiation has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 46 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1If I n = d n d x n x n ln x , then the value of 1 50 I 7 - 7 I 6 is equal to
  2. 2If f x = x + 1 ; x 1 0 ; x = 1 7 - 3 x ; x 1 then f ′ 0 equals to
  3. 3If y = log 10 ⁡ x + log x ⁡ 10 + log x ⁡ x + log 10 ⁡ 10 , then d y d x is equal to
  4. 4If f x = x 3 + 3 x + 1 and g x is the inverse function of f x , then the value of g ' 5 is equal to
  5. 5If y = 1 x , then the value of d y 1 + y 4 + d x 1 + x 4 + 3 is equal to
  6. 6If x = 3 cos ⁡ t and y = 5 sin ⁡ t , where t is a parameter, then 9 d 2 y d x 2 at t = - π 6 is equal to
  7. 7If the function f x = cos - 1 ⁡ x 3 2 - 1 - x - x 2 + x 3 (where, ∀ 0 x 1 ), then the value of 3 f ' 1 2 is equal to (take 3 = 1.73 )
  8. 8Let f x be a differentiable function on x ∈ R such that f x + y = f x ⋅ f y for all x , y . If f 0 ≠ 0 , f 5 = 12 and f ′ 0 = 16 , then f ′
  9. 9If l n x + y = 2 x y , then y ′ 0 is equal to
  10. 10If 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 to
  11. 11If y = a cos ( log x ) + b sin ( log x ) , where a b are parameters, then x 2 y + x y is equal to
  12. 12If f x = cos x . cos 2 x . cos 4 x . cos 8 x . cos 16 x , then f ' 4 is ( where f ' ( x ) = d dx f ( x ) )
  13. 13If y = tan ⁡ x - sin ⁡ x , then the value of d y d x at x = 5 π 4 is
  14. 14If x = 1 - t 2 1 + t 2 and y = 2 t 1 + t 2 , t h e n d y d x is equal to
  15. 15If f x = x 1 x 2 x 3 x 4 x 5 , then the value of f 5 is equal to
  16. 16Consider the function f x = t a n - 1 3 x - 2 3 + 2 x , ∀ x ≥ 0 . If g x is the inverse function of f x , then the value of g ′ π 4 is equal
  17. 17Let f x = x 2 - 4 x - 3 , x 2 and g ( x ) be the inverse of f ( x ) . Then the value of 1 g ' ( 2 ) , where f ( x ) = 2 , is (here, g ' repr
  18. 18If y = 1 + x y + s i n - 1 s i n 2 x , then d y d x at x = 0 is
  19. 19Let ϕ ( x ) be the inverse of the function f ( x ) and f ′ x = 1 1 + x 5 , then d d x ϕ x is equal to
  20. 20If f x = x - 4 x - 4 + t a n - 1 1 - 2 x 2 + x , 4 x 8 , then the value of f 5 is equal to
  21. 21The differential coefficient of log 10 ⁡ x with respect to log x 10 is
  22. 22Let y = x l o g e x . If the value of d y d x at x = e 4 is k , then the value of 4 e 3 k is (use e = 2.7 )
  23. 23If x = sec t + tan t and y = sec t - tan t , where t is a parameter, then the value of d y d x when x = 1 3 is
  24. 24If y = t a n - 1 x 1 + 6 x 2 + t a n - 1 2 x - 1 2 x + 1 ∀ x 0 , then d y d x is equal to
  25. 25If u = x 2 + y 2 and x = s + 3 t , y = 2 s - t , then d 2 u d s 2 is equal to (where t is a constant)
  26. 26If y = t a n - 1 s e c x - t a n x , then the value of d y d x is
  27. 27If y = s i n - 1 2 x 1 + x 2 , then d y d x is
  28. 28Let f x = t a n - 1 x 3 - 1 x 2 + x , then the value of 17 f 2 is equal to
  29. 29If y = cos ⁡ x cos ⁡ 2 x cos ⁡ 4 x cos ⁡ 8 x , then d y d x at x = π 2 is
  30. 30Consider a function f x = x x , ∀ x ∈ 1 , ∞ . If g x is the inverse function of f x , then the value of g ′ 4 is equal to
  31. 31If log 10 ⁡ x 3 - y 3 x 3 + y 3 = 2 , then d y d x =
  32. 32If x y . y x = 16 , then the value of d y d x at ( 2 , 2 ) is
  33. 33If f ( x ) = c o s - 1 s i n x 4 c o s 2 x - 1 , then 1 f ' 3 f 10 is
  34. 34The rate of change of ( x 2 + 16 ) with respect to x x - 1 at x = 3 is
  35. 35If ϕ x = log 8 ⁡ log 3 ⁡ x , then ϕ ′ e is equal to
  36. 36Let y = x x x … ∞ , then d y d x is equal to (given x 0 )
  37. 37If f x is a twice differentiable function such that f " x = - f x , f ' x = g x , h x = f 2 x + g 2 x and h 10 = 10 , then h 5 is equal to
  38. 38If y = 2 + sin ⁡ x + 2 + sin ⁡ x + 2 + sin ⁡ x + … ∞ , then the value of d y d x at x = 0 is
  39. 39If f x = 2 + x 1 + x 1 + x , then f ′ 0 is equal to
  40. 40If f x = 2 sin x - 1 - 2 cot x , then the value of f ' 3 is equal to
  41. 41If y = l n x x , then d 2 y d x 2 = 2 x 3 l n x - , where is
  42. 42If f x = s i n - 1 2 3 x 1 + 9 x , then f ' - 1 2 is equal to
  43. 43Let g x = x - 2 and h x = g g x be two functions, then the value of h ' - 1 + h ' 1 + h ' 3 + h ' 5 is equal to (where, h ' denotes the deri
  44. 44If y = t a n - 1 1 x 2 + x + 1 + t a n - 1 1 x 2 + 3 x + 3 + t a n - 1 1 x 2 + 5 x + 7 + t a n - 1 1 x 2 + 7 x + 13 , x 0 and d y d x x = 0
  45. 45If f : R R is a function defined as f x 3 = x 5 , x R - 0 and f x is differentiable x R , then the value of 1 4 f ' 27 is equal to (here f '
  46. 46Let f x is a differentiable function on x R , such that f x + y = f x f y for all x , y R where f 0 0 . If f 5 = 10 , f ' 0 = 6 , then the v

Frequently Asked Questions

1.How many questions are available for Differentiation?

This chapter includes 46 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

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

3.What is the difficulty level of Differentiation questions in NTA Abhyas (JEE Main)?

Of the 46 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Differentiation should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.