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Mathematics - Differentiation

Practise 10 JEE Advanced previous year questions on Differentiation, compiled from papers spanning 2006 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 Advanced tests.

Differentiation has been asked in 9 of the 27 years of JEE Advanced papers analysed (2000–2026), with 10 questions in all. 20% of them were easy, 40% moderate and 40% tough. Most of its questions came from 2008, with 2 questions that year. In the last three years (2024–2026) it had 2 questions across 6 papers, about 0.3 per paper.

The chapter's 3 topics are not weighted equally: Differentiation of composite functions (6 questions, 60%), Higher order derivatives (2 questions, 20%), and Differentiation of implicit functions (2 questions, 20%) have been asked the most. Differentiation of composite functions has also led over the last five years, with 1 question. Differentiation of composite functions has produced the most tough questions (3).

  1. 1Let denote the set of all real numbers. Consider the polynomial function defined by , for all . Here is the 10th order derivative of the fun2026 (Paper 2)Higher order derivatives
  2. 2Let denote the set of all real numbers. Let and be functions defined by , and Define the composite function by , where is the inverse of the2025 (Paper 2)Differentiation of composite functions
  3. 3Let f : R R , g : R R and h : R R be differentiable functions such that f x = x 3 + 3 x + 2 , g f x = x and h g g x = x , for all x R . Then2016 (Paper 1)Differentiation of composite functions
  4. 4Let f x = x sin x , x 0 . Then for all natural numbers n , f x vanishes at2013 (Paper 1)Differentiation of composite functions
  5. 5Let be a real-valued function defined on the interval such that for all and let be the inverse function of . Then is equal to2010 (Paper 2)Differentiation of composite functions
  6. 6If the function and , then the value of is2009 (Paper 2)Differentiation of composite functions
  7. 7Paragraph: Consider the functions defined implicitly by the equation on various intervals in the real line. If , the equation implicitly def2008 (Paper 1)Differentiation of implicit functions
  8. 8Paragraph: Consider the function defined by $f(x)= {x^2-a x+1}{x^2+a x+1} ; 0 Question: Which of the following is true ?2008 (Paper 2)Differentiation of implicit functions
  9. 9equals2007 (Paper 2)Higher order derivatives
  10. 10If , where is a continuous double differentiable function and . If and , then is2006Differentiation of composite functions

Frequently Asked Questions

1.How many questions are available for Differentiation?

This chapter includes 10 questions compiled from JEE Advanced papers spanning 2006 to 2026.

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

These are JEE Advanced 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 JEE Advanced Mathematics?

Differentiation has appeared in 9 of the 21 years of JEE Advanced papers covered here, with 10 questions across 10 papers - about one per paper it appears in.

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

Of the 10 questions analysed for this chapter, 20% are easy, 40% moderate and 40% tough. 2008 had the most, with 2 questions.

5.Which topics in Differentiation should I focus on?

These topics have carried the most weightage in Differentiation:

  • Differentiation of composite functions - 6 questions (60%)
  • Higher order derivatives - 2 questions (20%)
  • Differentiation of implicit functions - 2 questions (20%)
  • Differentiation of composite functions has produced the most tough questions (3).
6.Is Differentiation's weightage in JEE Advanced going up or down?

Across all 10 papers analysed, Differentiation has averaged about 1.0 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.