Page 150 - ADVANCED MATH F.5

Form Five Form Five

Differentiation

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Introduction
In this chapter, students will learn about derivatives, differentiation
of functions, applications of differentiation in real life problems,
Taylor’s and Maclaurin’s series, and an introduction to partial
derivatives of functions. Guide students to realize some common
methods of differentiation: first principles, power rule, chain rule,
product rule, quotient rule, and partial derivatives. Also, guide
students to determine the nature of stationary points, rates of
change between quantities, small changes in quantities, and series
expansions of different functions. The competencies developed
are applicable in various real life situations such as in business,
science, engineering, economics, building and constructions,
population modeling, and dynamical systems, among many other
applications.

Students’ activities
(a) Deducing the first principles method of differentiation
(b) Deriving the power rule method of differentiation
(c) Deriving the chain rule method of differentiation

(d) Deriving the product rule method of differentiation
(e) Deriving the quotient rule for differentiation
(f) Recognizing partial derivative
(g) Determining the nature of stationary points, rates of change
between quantities, small changes in quantities, and series
expansions of different functions

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ADVANCED MATH F.5 TG CHAPTERS.indd 144