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Comprehensive IGCSE Study Notes for Mathematics, Chemistry, Physics, and Economics
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In-Depth IGCSE Study Notes These comprehensive study notes are created to help you excel in your IGCSE exams. They cover key subjects including Mathematics, Chemistry, Physics, Economics, and more. Here’s what you’ll find in these notes: Detailed Summaries: Each topic is explained clearly...

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  • September 7, 2024
  • 2
  • 2024/2025
  • Class notes
  • Mr.sim
  • All classes

Subjects

  • add maths
  • igcse
  • gcse
  • exam preparations

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  • Secondary school
  • IGCSE Additional Mathematics
  • 1
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Differentiation: A Comprehensive Guide
1. Introduction to Differentiation

● Definition: Differentiation is the process of finding the rate of change of a function
concerning one of its variables.
● Notation:
○ dy/dx
○ f'(x)

2. Basic Rules of Differentiation

● Power Rule: For f(x) = x^n, f'(x) = nx^(n-1).
● Constant Rule: For a constant c, d/dx(c) = 0.
● Sum Rule: d/dx(f(x) + g(x)) = f'(x) + g'(x).

3. Product and Quotient Rules

● Product Rule: d/dx(u(x)v(x)) = u'(x)v(x) + u(x)v'(x).
● Quotient Rule: d/dx(u(x)/v(x)) = (v(x)u'(x) - u(x)v'(x)) /
(v(x))^2.

4. Chain Rule

● For a composite function f(g(x)), d/dx(f(g(x))) = f'(g(x)) * g'(x).

5. Applications of Differentiation

● Tangent and Normal: The slope of the tangent at a point is f'(x). The slope of the
normal is -1/f'(x).
● Stationary Points: Where f'(x) = 0.
○ Maximum: f''(x) < 0
○ Minimum: f''(x) > 0
○ Point of Inflection: f''(x) = 0

6. Second Derivative

● d²y/dx² is used to determine the concavity of the graph and the nature of stationary
points.

Practice Questions

1. Differentiate f(x) = 4x³ + 5x² - 3x + 7.

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