Page 155 - ADVANCED MATH F.5

Form Five Form Five

Derivative of product of polynomials
Teaching steps

1. Guide students through discussion to deduce the rule for
FOR ONLINE READING ONLY
differentiating the product of two functions u and v of the
independent variable x.

2. Assist students through discussion to obtain the product rule
dy = v du + u dv . Allow students to share alternative methods
dx dx dx
of deducing the product rule.

3. Use Examples 8.8 and 8.9 in the Student’s Book to guide
students to apply the product rule to differentiate the given
functions. Engage students to use mathematical software to

verify the solutions of the given problems. Advise them to share
their findings.

4. Instruct students to attempt Exercise 8.3 in the Student’s Book.
Advise students to submit their work. Check the correctness
of their answers, and provide them constructive feedback.
Encourage students to explore additional resources, such as

online tutorials, Symbolab, Mathematica or reference books, to
enrich their understanding and further practice.

Answers to Exercise 8.3

() 4x=
′
1. (a) fx 3 + 6x − 2
2
3
(b) fs ′ ( ) 24s + 60s + 64s − 32
2
=
′
2
−
3
(c) fy = − 96y + 36y + 96y − 27 3y − − 4 2y − 2
( )
(d) ft ′ ( ) 70t= 4 − 32t + 12t + 30t − 22
2
3
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Mathematics for Advanced Secondary Schools
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ADVANCED MATH F.5 TG CHAPTERS.indd 149