Exercise 13.2 Solutions - Class 11 Mathematics Unit 13 Differentiation

Step-by-step solved problems, theorem applications, and derivative rules for Exercise 13.2, Unit 13: Differentiation.Comprehensive solutions covering the Power Rule, Product Rule, and Quotient Rule for Punjab Board Class 11 (PCTB).

This page provides complete, step-by-step solved solutions for Exercise 13.2 of Unit 13: Differentiation for Class 11 Mathematics under the Punjab Board (PCTB / PECTAA). All problems on applying algebraic differentiation rules-including the constant rule (d/dx(c)=0), general power formula (d/dx(xⁿ)=nxⁿ⁻¹ for all real n), constant multiple rule, sum/difference rules, Leibniz Product Rule, and Quotient Rule on algebraic fractions-are thoroughly worked out for HSSC Part 1 exam success.
Back
Exercise 13.1
Next
Exercise 13.3
Advertisement

Exercise Overview

Exercise 13.2 equips students with the operational theorems and algebraic rules of Unit 13: Differentiation in Class 11 Mathematics, enabling rapid, analytical derivative calculation without resorting to lengthy first-principle limits.

The exercise systematically develops the foundational algebra of differential calculus: establishing that the derivative of any constant is zero (d/dx(c) = 0), extending the Power Rule d/dx(xⁿ) = n xⁿ⁻¹ across all real exponents (including negative and fractional powers), applying linearity through the constant multiple and sum/difference rules, and deploying the Leibniz Product Rule d/dx[u·v] = u·v' + v·u' alongside the Quotient Rule d/dx[u/v] = (v·u' - u·v')/v² for complex rational and radical functions.

In Punjab Board HSSC Part 1 examinations, Exercise 13.2 is among the most heavily weighted practical sections, forming the primary engine for Section B short questions and Section C multi-step algebraic long questions across Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, and other BISE boards. Fluency with these differentiation rules is indispensable for chain rules, implicit differentiation, higher-order derivatives, and practical optimization.

FAQs

Are these Exercise 13.2 solutions according to the Punjab Board syllabus?
Yes, these solutions strictly follow the official Punjab Curriculum and Textbook Board (PCTB / PECTAA) Class 11 Mathematics syllabus for Unit 13 (Differentiation) for the 2026-2027 academic session.
What are the key theorems and rules covered in Exercise 13.2 Class 11 Mathematics?
Exercise 13.2 covers core algebraic differentiation rules: Derivative of a Constant, Power Rule, Constant Multiple Rule, Sum and Difference Rule, Product Rule, and Quotient Rule.
What is the Power Rule for differentiation?
The Power Rule states that d/dx(xⁿ) = n xⁿ⁻¹ for any real number exponent n, allowing instantaneous differentiation of polynomial and radical functions.
What is the Constant Multiple Rule and why is d/dx(c) = 0?
The derivative of a constant function is zero because constants do not change. The Constant Multiple Rule states that d/dx[c f(x)] = c f'(x), factoring constants outside differentiation.
What is the Product Rule for finding the derivative of two multiplying functions?
The Product Rule states that d/dx[f(x) · g(x)] = f(x) g'(x) + g(x) f'(x), adding the product of the first function times the derivative of the second to the second times the derivative of the first.
What is the Quotient Rule and how is it applied to rational functions?
The Quotient Rule states that d/dx[f(x) / g(x)] = [g(x) f'(x) - f(x) g'(x)] / [g(x)]², subtracting the numerator's contribution from the denominator's and dividing by the square of the denominator.
Can students read these Exercise 13.2 solutions online?
Yes, students can read all Exercise 13.2 step-by-step differentiation solutions and rule applications directly online on MaryamNotes.pk on any web browser without downloading.
Are these Class 11 Exercise 13.2 notes completely free to access?
Yes, all solved notes, differentiation formulas, and step-by-step exercise guides on MaryamNotes.pk are 100% free and open-access for students and teachers across Pakistan.