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Summary

Differentiation – High School Calculus Summary Notes (UK Curriculum) – Key Rules, Derivatives & Graph Analysis

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2024/2025 Written for academic year
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Module Maths
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This document provides a compact and structured summary of differentiation rules and applications in calculus. It covers notation, first and second derivatives, the Chain Rule, and the geometric meaning of derivatives (tangents, normals, gradient). Additional sections explain increasing/decreasing functions, stationary points, and how to identify maximum, minimum, and inflection points. Ideal for GCSE or A-Level maths students needing a visual and concise reference for exam preparation.

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h7Differentiation

xn nx
1 Notations derivative f x derivative derivative
dya question




whenyoudifferentiateacertainequation thedifferentiatedequation ie becomestheformulaof
dye
atgradient
ChainRule d
eg derivativeof 3 2
x
0 3 2 u
a
3
tt
y

Ify f x isgraphofafunctionthen functionofthiscurve
dya fix isgradient
atpointA x wheretangent normalmeet is m thenequation tangentis given
of
Ifvalueof1 g by

y y m x X Thenormalatpoint x y isperpendiculartotangentsogradientofnormalis_em

ofnormalis
equation
yy Ym X x


1 FirstDerivativeofywithrespectto x

secondderivativeofywithrespecttox
112

48FurtherDifferentiation

DecreasingFunction f x valuesdecreasewhenever valuesincrease ygix

IncreasingFunction f x valuesincreasewhenever valuesincrease

whenf x o f x incr
fn x isincreasing aigy so for x a
whent x co f x
ifh x isdecreasingxcai.gg co taxca decreas



StationaryTurningPointApointwheregradientiszero

pointdYdx
MaximumPoint Gradientispositivetotheleft maxpoint negativetoright atmax
of
MinimumPoint Gradientisnegativetoits
left positivetotheright atminpointdydx o Wt
Connected book
image
Hugh Neill, Douglas Quadling, Julian Gilbey Cambridge International AS and A Level Mathematics: Pure Mathematics 1 Coursebook
Publisher: 2016 ISBN: 9781316600207 Edition: Unknown

Document information

Study
Other
School year
3
Summarized whole book?
No
Which chapters are summarized?
7 and 8
Uploaded on
May 9, 2025
Number of pages
2
Written in
2024/2025
Type
Summary
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