Differentiation — JEE Main Previous Year Questions

How many JEE Main questions come from Differentiation?

Differentiation has contributed 73 questions to Joint Entrance Examination (Main) papers between 2017 and 2026 — an average of about 7 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 73 questions carries a written, step-by-step solution, and each is tagged to Differentiation within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Differentiation questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 73 Differentiation questions (with full written solutions) are available in practice.

1. Question 1 · JEE Main 2019

   If ƒ(1) = 1, ƒ'(1) = 3, then the derivative of ƒ(ƒ(ƒ(x))) + (ƒ(x)) 2 at x = 1 is :
   1. (A)33
   2. (B)12
   3. (C)9
   4. (D)15
   Show answerAnswer

   Answer: (A) 33

2. Question 2 · JEE Main 2026

   Let $f(x)=x^3+x^2{f}^{\prime }(1)+2x{f}^{\prime \prime }(2)+f^{\prime \prime \prime }(3)$, $x\in \mathbb{R}$. Then the value of $f^{\prime }(5)$ is :
   1. (A)$\frac{657}{5}$
   2. (B)$\frac{117}{5}$
   3. (C)$\frac{2}{5}$
   4. (D)$\frac{62}{5}$
   Show answerAnswer

   Answer: (B) $\frac{117}{5}$

3. Question 3 · JEE Main 2026

   If $y={\tan }^{-1}\left(\frac{3\cos x-4\sin x}{4\cos x+3\sin x}\right)+2{\tan }^{-1}\left(\frac{x}{1+\sqrt{1-x^2}}\right)$, then $\frac{dy}{dx}$ at $x=\frac{\sqrt{3}}{2}$ is equal to :
   1. (A)3
   2. (B)-1
   3. (C)1
   4. (D)2
   Show answerAnswer

   Answer: (C) 1

4. Question 4 · JEE Main 2025

   $$\text{ If }y(x)=\left|\begin{array}{ccc}\sin x& \cos x& \sin x+\cos x+1\\ 27& 28& 27\\ 1& 1& 1\end{array}\right|,x\in \mathbb{R}\text{, then }\frac{d^{2}y}{d{x}^2}+y\text{ is equal to }$$
   1. (A)28
   2. (B)27
   3. (C)-1
   4. (D)1
   Show answerAnswer

   Answer: (C) -1

5. Question 5 · JEE Main 2025

   Let $f:(0,\infty )\to \mathbf{R}$ be a function which is differentiable at all points of its domain and satisfies the condition $x^2{f}^{\prime }(x)=2xf(x)+3$, with $f(1)=4$. Then $2f(2)$ is equal to :
   1. (A)19
   2. (B)23
   3. (C)29
   4. (D)39
   Show answerAnswer

   Answer: (D) 39

Differentiation questions by year

FAQs

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