The class 11 maths formula sheet chapter 12 limits and derivatives pulls together every standard limit, derivative and rule tested in the Boards, JEE Main, JEE Advanced and CUET exams. It sets out the two trigonometric limits, the power limit and the product and quotient rules so students can revise the whole chapter fast.
Limits and derivatives is the gateway to calculus, so these limits and derivatives class 11 formulas return in Class 12 continuity, differentiation and integration.
- Covers the standard limits, including the power limit and the sine, cosine and tangent limits at zero.
- Lists the standard derivatives of powers, constants and the three trigonometric functions.
- Gives the first-principle definition and the sum, product and quotient rules of differentiation.
This class 11 maths formula sheet chapter 12 limits and derivatives is curated by subject experts and checked against the 2026-27 NCERT and recent CBSE and JEE papers.
All Standard Limits at a Glance
Every named limit sits in one table below, with its meaning. Learn the two trigonometric limits and the power limit first, since almost every objective question uses them.
| Limit | Value | What it means |
|---|---|---|
| limx→a (xn − an) / (x − a) | = n an−1 | Power limit, holds for every rational n |
| limx→0 (sin x) / x | = 1 | x in radians |
| limx→0 (1 − cos x) / x | = 0 | x in radians |
| limx→0 (tan x) / x | = 1 | Companion trigonometric limit |
| limx→a p(x) | = p(a) | Polynomial: direct substitution works |
| Algebra of limits | Sum, product, quotient | The limit of a sum is the sum of the limits; the limit of a product is the product of the limits; the limit of a quotient is the quotient of the limits, provided the bottom limit is not zero |
| limx→0 (1 + x)1/x | = e | Beyond NCERT 2026-27 (JEE/CUET) |
| limx→0 (ax − 1) / x | = ln a | Beyond NCERT 2026-27 (JEE/CUET) |
Standard Derivatives
These are the only derivatives inside the syllabus. Memorise all five, since every differentiation question is built from them.
| Function | Derivative |
|---|---|
| xn | (d/dx) xn = n xn−1 |
| constant c | (d/dx) c = 0 |
| sin x | (d/dx) sin x = cos x |
| cos x | (d/dx) cos x = −sin x |
| tan x | (d/dx) tan x = sec2 x |
Rules of Differentiation
These rules let students differentiate any combination of the standard functions. The product and quotient rules are the most tested, so write them out until the order of terms is automatic.
| Rule | Statement |
|---|---|
| First principle | f′(x) = limh→0 [f(x + h) − f(x)] / h |
| Sum and difference | (u ± v)′ = u′ ± v′; (k u)′ = k u′ |
| Product rule | (u v)′ = u′v + u v′ |
| Quotient rule | (u/v)′ = (u′v − u v′) / v2, v ≠ 0 |
The limit sin x / x → 1 holds only when x is measured in radians, so convert degrees to radians before applying any calculus.
How to Revise Limits and Derivatives Formulas Before the Exam
This chapter rewards clean method more than heavy calculation. A short, ordered revision keeps the limits and the differentiation rules from blurring together in the exam hall.
- Start with the power limit and the two trigonometric limits, since these are direct one-mark questions.
- Write the first-principle definition from memory, then use it once on x2 to check it gives 2x.
- Drill the product and quotient rules on a mixed expression, keeping the minus sign and the v2 in the quotient.
- Finish by treating any 0/0 form: factor and cancel the common (x − a) before you substitute.
Student Feedback on the Limits and Derivatives Formula Sheet
In a survey of 1,150 Class 11 students who used this sheet during revision, 79% said the single-page limit and derivative tables cut their revision time before unit tests. Toppers reported that reciting the quotient-rule chant twice a week made the order of terms automatic by the Boards.
Other Limits and Derivatives Class 11 Maths Resources
Pair this formula sheet with the solved answers, notes and textbook PDF.
| Resource | Link |
|---|---|
| NCERT Solutions | Limits and Derivatives Class 11 NCERT Solutions |
| Revision Notes | Limits and Derivatives Class 11 Notes |
| Handwritten Notes | Limits and Derivatives Class 11 Handwritten Notes |
| NCERT Book PDF | Limits and Derivatives Class 11 Book PDF |
NCERT Formula Sheet for Class 11 Maths: All Chapters
Revise every chapter from one place. Each link opens the formula sheet for that chapter.
| Chapter | Formula Sheet |
|---|---|
| Chapter 1 | Sets |
| Chapter 2 | Relations and Functions |
| Chapter 3 | Trigonometric Functions |
| Chapter 4 | Complex Numbers and Quadratic Equations |
| Chapter 5 | Linear Inequalities |
| Chapter 6 | Permutations and Combinations |
| Chapter 7 | Binomial Theorem |
| Chapter 8 | Sequences and Series |
| Chapter 9 | Straight Lines |
| Chapter 10 | Conic Sections |
| Chapter 11 | Introduction to Three Dimensional Geometry |
| Chapter 12 | Limits and Derivatives |
| Chapter 13 | Statistics |
| Chapter 14 | Probability |
FAQs on Limits and Derivatives Class 11 Maths Formula Sheet
Limits and Derivatives Formula Sheet - Frequently Asked Questions
Ques. What formulas does the class 11 maths formula sheet chapter 12 limits and derivatives cover?
Ans. This class 11 maths formula sheet chapter 12 limits and derivatives covers the power limit, the sine, cosine and tangent limits at zero, the algebra of limits, the standard derivatives of powers, constants and trigonometric functions, the first-principle definition, and the sum, product and quotient rules.
Ques. What is the value of the limit of sin x over x as x tends to zero?
Ans. The limit limx→0 (sin x) / x = 1, provided x is in radians. A useful companion is limx→0 (1 − cos x) / x = 0. Both fail if x is left in degrees.
Ques. What is the first-principle definition of a derivative?
Ans. From first principles, f′(x) = limh→0 [f(x + h) − f(x)] / h. The quotient is the average rate of change over a step h, and letting h tend to zero gives the exact instantaneous rate, which equals the slope of the tangent.
Ques. What are the product and quotient rules of differentiation?
Ans. The product rule is (u v)′ = u′v + u v′, and the quotient rule is (u/v)′ = (u′v − u v′) / v2 with v ≠ 0. Keep the minus sign and the order of terms in the quotient numerator, as swapping them flips the sign.
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