Unit 13 Class 11 Math Notes – Differentiation (Punjab Board New Book)
Unit 13 (Chapter 13) Class 11 Math Notes – Differentiation: step-by-step solutions of Exercise 13.1, Exercise 13.2 and Exercise 13.3 for the Punjab Board new book (1st Year). Tap an exercise below to open its PDF solution, then view it online or download it.
This unit is part of our Class 11 maths notes for the Punjab Board new book, where you can open the solutions of the other units.
Exercise Wise Solutions of Unit 13 Class 11 Math
What Each Exercise of Unit 13 Covers
Exercise 13.1 – Derivative from First Principles
Exercise 13.1 has 12 questions on differentiation from first principles, gradients, tangent lines, and average and instantaneous velocity.
Exercise 13.2 – Rules of Differentiation
Exercise 13.2 has 5 questions on the power, product, quotient and chain rules, including two “show that” proofs.
Exercise 13.3 – Rates of Change
Exercise 13.3 has 8 questions on rates of change: velocity, acceleration, marginal profit, investment growth, bridge and beam stress, and tank cost.
Key Formulas of Unit 13 Class 11 Math
- \(\dfrac{dy}{dx}=\displaystyle\lim_{\delta x\to0}\dfrac{\delta y}{\delta x}\)
- \(\dfrac{d}{dx}x^n=nx^{n-1}\)
- Product rule: \((fg)’=f’g+fg’\).
- Quotient rule: \(\left(\dfrac fg\right)’=\dfrac{f’g-fg’}{g^2}\).
- Velocity \(v=\dfrac{ds}{dt}\), acceleration \(a=\dfrac{dv}{dt}\).
Related Class 11 Math Notes
Continue with Unit 12 Class 11 Math Notes and Unit 14 Class 11 Math Notes, or go back to the Class 11 maths notes hub for all 14 units.
FAQs About Unit 13 Class 11 Math
How many exercises are there in Unit 13?
Unit 13 has three exercises: Exercise 13.1, 13.2 and 13.3.
What does “first principle” mean in differentiation?
It means finding the derivative directly from the definition, as the limit of \(\dfrac{f(x+h)-f(x)}{h}\) as \(h\to0\), without using the rules of differentiation.
Are these notes for the new book?
Yes. These solutions are for the new Class 11 mathematics book by PECTAA (2025 edition onwards), used by the nine BISE Punjab boards: Lahore, Gujranwala, Faisalabad, Multan, Rawalpindi, Sargodha, Sahiwal, Bahawalpur and Dera Ghazi Khan.