IP AMaths Notes (Upper Sec, Year 3-4): 14) Differentiation Fundamentals
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First principles, power rule, and basic derivative interpretations for IP AMaths.
Last updated 30 Nov 2025
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- Start Here
- 1 Key rules
- 2 Worked example - From first principles
- 3 Worked example - Composite function
Q: What does IP AMaths Notes (Upper Sec, Year 3-4): 14) Differentiation Fundamentals cover?
A: First principles, power rule, and basic derivative interpretations for IP AMaths.
Differentiation measures instantaneous rate of change. Know how to move from first principles to the standard rules.
Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.
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Content here mirrors the SEAB GCE O-Level Additional Mathematics (4049) differentiation fundamentals: limits from first principles, power rule, and basic gradient/tangent interpretation.
Status: SEAB O-Level Additional Mathematics 4049 syllabus (exams from 2025) checked 2025-11-30 - scope unchanged; remains the reference for this note.
Start Here
| Read time | What to take away |
| 1 second | Differentiation measures instantaneous rate of change. |
| 10 seconds | Learn what the derivative means before memorising rules: it gives gradient, tangent slope, and rate of change. |
| 100 seconds | Example: for y = x^2, first principles gives gradient 2x; at x = 3, the tangent gradient is 6. |
1 Key rules
Limit definition.
