JEE Main · Maths · Continuity and Differentiability
Chain Rule: JEE Main previous year questions
31 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Asked most years. 9 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 31
- in 30 of 108 shifts
- Years asked
- 6/8
- last asked 2025
- Weighted estimate
- 0.2
- model; history: 0.2 a shift on average, typically 0.0–0.4
Key findings
- 01
Asked in 6 of 8 years with analysed shifts and in 30 of 108 shifts: 31 questions, #107 of 196 topics. Last asked in 2025.
- 02
52% of its questions since 2020 tested an idea no earlier year had asked; 6 repeated an idea from the year before.
- 03
The most repeated idea is Second Order Implicit Chain Rule, asked 5 times in 5 shifts (2020, 2021, 2022, 2024), most often as “second derivative relation from inverse trig function”.
- 04
JEE Main has asked 15 of the 60 ideas in this topic; 39 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (74%); 26% need a numerical answer, 10% are easy and 35% hard.
- 06
The skill tested most is multi-step (61%), then calculation (35%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 0 in 1 shift · 2020: 6 in 12 shifts · 2021: 4 in 24 shifts · 2022: 9 in 24 shifts · 2023: 3 in 12 shifts · 2024: 8 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.
- Up to 2023
- 0.2
- a shift, of 25
- Since 2024
- 0.2
- -0.1
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 30/108
- 28% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 31 questions on Chain Rule since 2017.
Difficulty
QUESTIONS- Easy3 · 10%
- Medium17 · 55%
- Hard11 · 35%
Format
SHARE- Single correct · 23 Q74%
- Numerical value · 8 Q26%
Skill tested
SHARE- Multi-step · 19 Q61%
- Calculation · 11 Q35%
- Application · 1 Q3%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 15 of the 60 ideas in this topic. 39 have never been asked yet.
- Asked directly15 · 25%
- Touched inside another question6 · 10%
- Never asked39 · 65%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
12 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
15 different ideas were tested; 8 came more than once.
second derivative relation from inverse trig function
Single correct · 5 shifts · 2 numericalrelated rates of sphere surface area and radius
Single correct · 5 shifts · 1 numericalderivative of inverse function at a point
Single correct · 4 shiftsderivative of determinant function
Single correct · 2 shiftsderivatives of trig quotient at a point
Single correct · 2 shiftsevaluate derivative from functional recurrence
Single correct · 2 shiftsderivative expression on implicit curve
Numerical value · 2 shifts · 1 numericalderivative of composite inverse trig function
Numerical value · 2 shifts · 2 numericalvalue of derivative at a point
Numerical value · 1 shift · 1 numericalderivative of determinant function at a point
Single correct · 1 shiftderivative at a point of complicated product
Single correct · 1 shiftderivative of implicit function with variable exponents
Single correct · 1 shiftsecond derivative of parametric curve
Single correct · 1 shiftderivative value at a point
Single correct · 1 shiftsecond derivative of inverse of power tower
Numerical value · 1 shift · 1 numerical
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Second Order Implicit Chain Rulesecond derivative relation from inverse trig function | 5 | 5 | Single correctMulti-step | 2 | |
| Chain Rule in Related Ratesrelated rates of sphere surface area and radius | 5 | 5 | Single correctMulti-step | 1 | |
| Derivative of Inverse Functions via Chain Rulederivative of inverse function at a point | 4 | 4 | Single correctMulti-step | – | |
| Differentiating Determinants via Chain Rulederivative of determinant function | 2 | 2 | Single correctCalculation | – | |
| Second Derivative of Composite Functionsderivatives of trig quotient at a point | 2 | 2 | Single correctMulti-step | – | |
| Differentiating Functional Equationsevaluate derivative from functional recurrence | 2 | 2 | Single correctMulti-step | – | |
| Implicit Chain Rulederivative expression on implicit curve | 2 | 2 | Numerical valueCalculation | 1 | |
| Pre-simplification via Trig Substitutionderivative of composite inverse trig function | 2 | 2 | Numerical valueMulti-step | 2 | |
| Chain Rule for Trigonometric Powers and Argumentsvalue of derivative at a point | 1 | 1 | Numerical valueCalculation | 1 | |
| Chain Rule in Determinantsderivative of determinant function at a point | 1 | 1 | Single correctCalculation | – | |
| Product Rule with Chain Rulederivative at a point of complicated product | 1 | 1 | Single correctMulti-step | – | |
| Logarithmic Differentiation of Composite Productsderivative of implicit function with variable exponents | 1 | 1 | Single correctCalculation | – | |
| Chain Rule in Parametric Differentiationsecond derivative of parametric curve | 1 | 1 | Single correctCalculation | – | |
| Derivative of Variable Base Logarithmsderivative value at a point | 1 | 1 | Single correctCalculation | – | |
| Logarithmic Differentiation for Power Towerssecond derivative of inverse of power tower | 1 | 1 | Numerical valueMulti-step | 1 |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Chain Rule questions, year by year
The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.
JEE Main 20251 question in 1 shift
- 3 Apr, Shift 1Q16If , , then…
Idea: Differentiating Determinants via Chain Rule
Asked the year beforeMediumSingle correct
JEE Main 20248 questions in 8 shifts
- 4 Apr, Shift 1Q11Let for all . Consider a function such that for all .…
Idea: Derivative of Inverse Functions via Chain Rule
MediumSingle correct - 5 Apr, Shift 1Q8Let , , and be a function such that for all . Then…
Idea: Derivative of Inverse Functions via Chain Rule
MediumSingle correct - 5 Apr, Shift 2Q20If , then at ,…
Idea: Second Derivative of Composite Functions
Asked the year beforeHardSingle correct - 9 Apr, Shift 2Q8If , then at is equal to
Idea: Second Order Implicit Chain Rule
MediumSingle correct - 1 Feb, Shift 2Q25If , then is…
Idea: Chain Rule for Trigonometric Powers and Arguments
New ideaHardNumerical value - 29 Jan, Shift 1Q9Suppose . Then the value of is equal to
Idea: Product Rule with Chain Rule
New ideaHardSingle correct - 30 Jan, Shift 1Q4If…
Idea: Differentiating Determinants via Chain Rule
New ideaMediumSingle correct - 31 Jan, Shift 1Q3If for all , then…
Idea: Chain Rule in Determinants
New ideaMediumSingle correct
JEE Main 20233 questions in 3 shifts
- 6 Apr, Shift 1Q9If , then at is equal to:
Idea: Logarithmic Differentiation of Composite Products
New ideaMediumSingle correct - 8 Apr, Shift 1Q19Let , . Then…
Idea: Second Derivative of Composite Functions
New ideaHardSingle correct - 13 Apr, Shift 1Q1For the differentiable function , let , then…
Idea: Differentiating Functional Equations
MediumSingle correct
JEE Main 20229 questions in 8 shifts
- 26 Jul, Shift 2Q8The value of at is
Idea: Derivative of Variable Base Logarithms
New ideaMediumSingle correct - 27 Jul, Shift 2Q25A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is…
Idea: Chain Rule in Related Rates
MediumNumerical value - 27 Jul, Shift 2Q26For the curve , the value of , at the point , ,…
Idea: Implicit Chain Rule
HardNumerical value - 28 Jul, Shift 2Q68Let and . Then…
Idea: Chain Rule in Parametric Differentiation
New ideaHardSingle correct - 24 Jun, Shift 1Q3The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3…
Idea: Chain Rule in Related Rates
MediumSingle correct - 25 Jun, Shift 1Q6Let be defined as If is a function such that , 'x'…
Idea: Derivative of Inverse Functions via Chain Rule
EasySingle correct - 25 Jun, Shift 2Q11Water is being filled at the rate of in a right circular conical vessel (vertex downwards) of height 35…
Idea: Chain Rule in Related Rates
MediumSingle correct - 27 Jun, Shift 1Q8If , , then :
Idea: Second Order Implicit Chain Rule
Asked the year beforeMediumSingle correct - 27 Jun, Shift 2Q26If , , then at is equal to ___________.
Idea: Logarithmic Differentiation for Power Towers
New ideaHardNumerical value
JEE Main 20214 questions in 4 shifts
- 26 Aug, Shift 1Q86If is an implicit function of such that , then at is equal to __________.
Idea: Second Order Implicit Chain Rule
Asked the year beforeMediumNumerical value - 27 Aug, Shift 1Q84If , and , then is equal to __________.
Idea: Second Order Implicit Chain Rule
Asked the year beforeHardNumerical value - 16 Mar, Shift 2Q79Let where be a twice differentiable function such that . If be defined as…
Idea: Differentiating Functional Equations
New ideaHardSingle correct - 17 Mar, Shift 1Q89If and its first derivative with respect to is…
Idea: Pre-simplification via Trig Substitution
Asked the year beforeHardNumerical value
JEE Main 20206 questions in 6 shifts
- 9 Jan, Shift 1Q59A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at a rate of…
Idea: Chain Rule in Related Rates
New ideaMediumSingle correct - 9 Jan, Shift 2Q60Let and be differentiable functions on such that is the identity function. If for some ,…
Idea: Derivative of Inverse Functions via Chain Rule
New ideaEasySingle correct - 2 Sep, Shift 2Q72If , then at is ________.
Idea: Pre-simplification via Trig Substitution
New ideaHardNumerical value - 3 Sep, Shift 1Q57If , , then :
Idea: Second Order Implicit Chain Rule
New ideaMediumSingle correct - 3 Sep, Shift 2Q59If the surface area of a cube is increasing at a rate of 3.6 cm/sec, retaining its shape; then the rate of change of its volume (in…
Idea: Chain Rule in Related Rates
New ideaEasySingle correct - 4 Sep, Shift 1Q59If , where , then at…
Idea: Implicit Chain Rule
New ideaMediumSingle correct
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.