Introduction
The best Unit 13, Differentiation, solved notes for Class 11 Punjab Boards are now available, with 100 percent of exercises solved using easy, step by step solutions, graphs, diagrams, and the marking scheme, based on the new book from PECTAA, the Punjab Curriculum and Textbook Board. These notes are perfect for the 2026 exams and are built to help students score 90 plus marks.
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Ideal for Students, Teachers, and Lecturers Across All Nine Punjab Boards
These notes are used at top registered institutions across all nine Punjab boards, including Aitchison College Lahore (Lahore Board), Sadiq Public School Bahawalpur (Bahawalpur Board), Army Public Schools (Rawalpindi and Multan Boards), Beaconhouse Schools (Faisalabad and Gujranwala Boards), Forman Christian College Lahore (Lahore Board), Government College University Faisalabad (Faisalabad Board), Cadet College Hasan Abdal (Rawalpindi Board), Cadet College Petaro.
Cadet College Okara (Sahiwal Board), Cadet College Kohat, Cadet College Sargodha (Sargodha Board), Cadet College Jhang (Faisalabad Board), Cadet College Pasrur (Gujranwala Board), Cadet College Spinkai (DG Khan Board), Military College Jhelum (Rawalpindi Board), Garrison Cadet College Kohat, and many more.
What’s Inside Unit 13, Building the Derivative From the Ground Up
Unit 13 takes the limit concept from Unit 12 and puts it to work, building the derivative first from raw definition, then handing students faster tools once the underlying idea is solid.
It opens with the derivative by definition, using the limit definition f'(x) = lim h→0 [f(x + h) − f(x)]/h to compute derivatives directly, which forces a real understanding of what a derivative represents before any shortcut rules are introduced.
From there, the unit moves into the power rule and basic differentiation rules, covering derivatives of polynomial terms, constants, and sums or differences of functions, the fastest and most frequently used tools in the entire unit.
This is followed by the product rule and quotient rule, used when differentiating the product or quotient of two functions that can’t simply be multiplied or divided out first, along with the algebraic simplification that typically follows.
The unit then introduces the chain rule, for differentiating a function nested inside another function, a technique that becomes essential once functions stop being simple polynomials and start involving roots, powers of expressions, and composite forms.
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It closes with implicit differentiation, used when y cannot be easily isolated on one side of an equation, differentiating both sides of the equation with respect to x and solving algebraically for dy/dx.
Exercise 13.1, Derivative by Definition, Fully Solved
All questions in Exercise 13.1 are fully solved, covering finding the derivative of a function directly from the limit definition.
| Question | Function | Derivative |
|---|---|---|
| Q1(i) | f(x) = 2x² + 1 | f'(x) = 4x |
| Q1(ii) | f(x) = 2 − √x | f'(x) = −1/(2√x) |
| Q1(iii) | f(x) = 1/√x | f'(x) = −1/(2x^(3/2)) |
The full solved PDF for Exercise 13.1 is available, covering every question and part in complete detail.
Exercise 13.2, The Power Rule and Basic Differentiation, Fully Solved
Exercise 13.2 is fully solved, covering differentiating polynomial and power functions using the power rule, along with the rules for constants and sums or differences of functions.
Exercise 13.3, Product Rule and Quotient Rule, Fully Solved
Exercise 13.3 is fully solved, covering differentiating products and quotients of two or more functions, followed by full algebraic simplification of the resulting derivative.
Bonus Resources
- A Differentiation formula sheet PDF for quick reference.
- The top 30 derivative rules and definition shortcuts for faster problem solving.
- Differentiation video lectures.
Why This Unit Matters for Your Overall Score
Differentiation is arguably the single most important unit in the Class 11 syllabus, since nearly every later chapter, from curve sketching to optimization to rates of change, depends on the rules built here. Working through Exercise 13.1 by hand, using the actual limit definition rather than jumping straight to shortcuts, is what makes the power, product, and quotient rules in Exercises 13.2 and 13.3 feel like natural consequences rather than arbitrary formulas.
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Frequently Asked Questions
Which exercises are covered in these Unit 13 notes?
Exercise 13.1 through Exercise 13.5 are covered in full, along with the Unit 13 Review Exercise, spanning derivatives by definition, the power rule, the product and quotient rules, the chain rule, and implicit differentiation.
When do I need the chain rule instead of the power rule?
Use the chain rule whenever the function being differentiated is a function nested inside another function, such as (3x + 1)⁵ or √(x² + 1). If the expression is a single variable raised to a power with nothing more complex inside it, the plain power rule is enough.
Conclusion
With Exercise 13.1 through Exercise 13.5 and the Review Exercise fully solved, Class 11 students across all nine Punjab boards have a complete, exam ready resource for mastering Differentiation ahead of the 2026 exams. Use these notes alongside the bonus formula sheet, shortcuts, and past papers to build both speed and accuracy for your Mathematics exam.
Best of luck for your Class 11 Mathematics exam!