Summary O Level Additional Mathematics Chapter on Differentiation
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Course
Cambridge IGSCE
Institution
Cambridge IGSCE
Book
Additional Mathematics for O Level
This document provides a comprehensive explanation of the chapter on Differentiation for the Cambridge O Level Additional Mathematics Syllabus 4037. It can also be used for similar syllabi such as EDXCEL, International Baccalaureate, ZIMSEC, etc. It also has practice questions.
• understand the idea of a derived function
ð£ ðl £ ð ð£
• use the notations 𝑓 F (𝑥 ), 𝑓′′(𝑥), , H= x yI
ðT ðT l ðT ðT
•
• use the derivatives of the standard functions 𝑥 (for any rational 𝑛),
sin𝑥, cos 𝑥, tan 𝑥, 𝑒 T , ln 𝑥, together with constant multiples, sums
and composite functions of these
• differentiate products and quotients of functions
• apply differentiation to gradients, tangents and normals, stationary
points, connected rates of change, small increments and
approximations and practical maxima and minima problems
• use the first and second derivative tests to discriminate between
maxima and minima
• apply differentiation to kinematics problems that involve
displacement, velocity and acceleration of a particle moving in a
straight line with variable or constant acceleration, and the use of 𝑥– 𝑡
and 𝑣– 𝑡 graphs
Calculus
Calculus is the study of change in variables. Important techniques in calculus
include differentiation and integration.
What is differentiation?
226
,Differentiation is the process of determining the rate of change of a function
with respect to a variable at an instantaneous point. The derivative of a
function is its gradient function, so the value of the derivative at a point
represents the gradient of the graph at that point.
Given 𝑦 = 𝑓(𝑥) then the first derivative of 𝑦 with respect to 𝑥 equals the
first derivative of 𝑓(𝑥) which is written in the following notation:
𝑑𝑦
= 𝑓 F (𝑥)
𝑑𝑥
ð£
Where is the rate of change in 𝑦 with respect to 𝑥 (pronounced 𝑑𝑦 by 𝑑𝑥)
ðT
and 𝑓 F (𝑥) is the first derivative of 𝑓(𝑥) and is pronounced as such.
Basic rules of differentiation
1. If a function is the sum or difference of other functions, then the
derivative is also the sum or difference of the derivatives of those
functions i.e.:
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