IGCSE Differentiation: Complete Guide for Cambridge IGCSE Mathematics

IGCSE differentiation is an advanced calculus topic in Cambridge IGCSE Mathematics that appears in Paper 4 (Extended). Mastering differentiation rules, finding derivatives, and gradient of curves is essential for achieving top grades in IGCSE exams.

This comprehensive IGCSE differentiation guide covers everything you need to know, including basic differentiation rules, finding gradients, stationary points, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to differentiate polynomial functions, find gradients of curves, identify stationary points, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Additional Mathematics practice deck featuring exam-style questions and instant feedback.

---

Why IGCSE Differentiation Matters

IGCSE differentiation is an essential calculus topic. Here’s why it’s so important:

• High frequency topic: Differentiation questions appear regularly in IGCSE Extended papers
• Foundation skill: Essential for advanced mathematics and calculus
• Exam weight: Typically worth 6-12 marks per paper
• Real-world applications: Used in physics, engineering, and optimization problems
• Problem-solving skills: Develops understanding of rates of change and gradients

Key insight from examiners: Students often struggle with the power rule or make errors with negative powers. This guide will help you master these systematically.

---

Understanding Differentiation

Differentiation finds the rate of change of a function. The derivative dy/dx gives the gradient of the curve at any point.

---

Basic Differentiation Rules

Power Rule

If y = x^n, then dy/dx = nx^(n-1)

Example 1: Differentiate y = x³

Solution: dy/dx = 3x²

Answer: 3x²

Example 2: Differentiate y = x⁵

Solution: dy/dx = 5x⁴

Answer: 5x⁴

---

Constant Rule

If y = c (constant), then dy/dx = 0

Example 3: Differentiate y = 7

Solution: dy/dx = 0

Answer: 0

---

Multiple Terms

Differentiate each term separately.

Example 4: Differentiate y = 3x² + 5x - 2

Solution: dy/dx = 6x + 5

Answer: 6x + 5

---

Finding Gradients

Substitute the x-value into the derivative to find the gradient at that point.

Example 5: Find the gradient of y = x² + 3x at x = 2

Solution: dy/dx = 2x + 3 At x = 2: gradient = 2(2) + 3 = 7

Answer: 7

---

Stationary Points

Stationary points occur where dy/dx = 0

Example 6: Find the stationary point of y = x² - 4x + 3

Solution: dy/dx = 2x - 4 Set dy/dx = 0: 2x - 4 = 0, so x = 2 Substitute: y = (2)² - 4(2) + 3 = -1 Stationary point: (2, -1)

Answer: (2, -1)

---

Common Examiner Traps

• Power rule errors - Remember: multiply by power, then reduce power by 1
• Forgetting constants - Constants differentiate to 0
• Sign errors - Watch positive/negative signs carefully
• Stationary point errors - Always substitute back to find y-coordinate

---

Practice Questions

Question 1

Differentiate y = 4x³ - 2x² + x - 5

Solution: dy/dx = 12x² - 4x + 1

Answer: 12x² - 4x + 1

---

Tutopiya Advantage: Personalised IGCSE Differentiation Coaching

• Live whiteboard walkthroughs of differentiation problems
• Exam-docket homework packs mirroring CAIE specimen papers
• Analytics dashboard so parents see accuracy by topic
• Flexible slots with ex-Cambridge markers for last-mile polishing

📞 Ready to turn shaky differentiation skills into exam-ready confidence? Book a free IGCSE maths trial and accelerate your revision plan.

---

Frequently Asked Questions About IGCSE Differentiation

What is differentiation?

Differentiation finds the rate of change of a function. The derivative gives the gradient of the curve.

What is the power rule?

If y = x^n, then dy/dx = nx^(n-1). Multiply by the power, then reduce the power by 1.

How do I find the gradient at a point?

Differentiate the function, then substitute the x-value into the derivative.

What are stationary points?

Stationary points occur where dy/dx = 0 - these are maximum, minimum, or point of inflection.

---

Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Graphs of Functions: Complete Guide - Master function graphs
• IGCSE Quadratic Functions: Complete Guide - Master quadratic functions
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

---

Next Steps: Master IGCSE Differentiation with Tutopiya

Ready to excel in IGCSE differentiation? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
• Interactive whiteboard sessions for visual learning
• Progress tracking to identify and strengthen weak areas
• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master differentiation and achieve your target grade.

---