JEE Main Maths · Continuity and Differentiability

Chain Rule in JEE Main

Name: Chain Rule: JEE Main previous year questions
Creator: Lumi

Chain Rule (Maths, Continuity and Differentiability) came 8 times in 8 of the 42 JEE Main shifts Lumi analysed, across 8 distinct ideas. 4 of them came in 2024–26; it was last asked in 2025.

Questions: 8; in 8 shifts
Ideas asked: 8; 0 asked more than once
Numerical answer: 0; 0% of its questions
Pattern: Asked most years; last asked 2025

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 1Medium 5Hard 2

Format

Single correct8 Q

Ideas inside the topic

8 ideas

Chain Rule in Determinants1 Q
Differentiating Determinants via Chain Rule1 Q
Differentiating Functional Equations1 Q
Second Order Implicit Chain Rule1 Q
Derivative of Inverse Functions via Chain Rule1 Q
Logarithmic Differentiation of Composite Products1 Q
Product Rule with Chain Rule1 Q
Chain Rule in Related Rates1 Q

Where it sits

Part of Continuity and Differentiability, which had 48 questions in all. Chain Rule accounts for 17% of them. In Lumi's JEE taxonomy it belongs to Calculus.

Some questions sit in other chapters too: Application of Derivatives, Determinants.

Every question

All 8 Chain Rule questions

Newest first, each with its options and official answer.

3 Apr 2025, Shift 1 · Q16If $y(x) = \begin{vmatrix} \sin x & \cos x & \sin x + \cos x + 1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{vmatrix}$ , $x \in \mathbb{R}$ , then…MediumSingle correct
9 Apr 2024, Shift 2 · Q8If $\log_e y=3\sin^{-1}x$ , then $(1-x^2)y''-xy'$ at $x=\frac{1}{2}$ is equal toMediumSingle correct
29 Jan 2024, Shift 1 · Q9Suppose $f(x)=\frac{(2^x+2^{-x})\tan x\sqrt{\tan^{-1}(x^2-x+1)}}{(7x^2+3x+1)^3}$ . Then the value of $f'(0)$ is equal toHardSingle correct
31 Jan 2024, Shift 1 · Q3If $f(x)=\begin{vmatrix}x^3 & 2x^2+1 & 1+3x\\ 3x^2+2 & 2x & x^3+6\\ x^3-x & 4 & x^2-2\end{vmatrix}$ for all $x\in\mathbb{R}$ , then…MediumSingle correct
6 Apr 2023, Shift 1 · Q9If $2x^y+3y^x=20$ , then $\frac{dy}{dx}$ at $(2,2)$ is equal to:MediumSingle correct
24 Jun 2022, Shift 1 · Q3The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3…MediumSingle correct
16 Mar 2021, Shift 2 · Q79Let $f:S\to S$ where $S=(0,\infty)$ be a twice differentiable function such that $f(x+1)=xf(x)$ . If $g:S\to\mathbf R$ be defined as…HardSingle correct
9 Jan 2020, Shift 2 · Q60Let $f$ and $g$ be differentiable functions on $\mathbf{R}$ such that $f\circ g$ is the identity function. If for some $a,b\in\mathbf{R}$ ,…EasySingle correct