Page 158 - ADVANCED MATH F.5

Form Five Form Five

The chain rule
Teaching steps

1. Design a strategy which will engage students in deducing the
chain rule for differentiating of a composite function y = fu
()
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where u itself is a function of x.
2. Assist students through discussion to obtain the chain rule
dy = dy × du .Allow students to share alternative methods of
dx du dx
deducing the chain rule.
3. Use Examples 8.12, 8.13, and 8.14 in the Student’s Book to
guide students to apply the chain rule to differentiate the given
functions. Engage students to use scientific calculators and
mathematical software to verify the solutions for the given
examples. Advise them to share their findings.

4. Instruct students to attempt Exercise 8.5 in the Student’s Book.
Advise students to submits 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 practice further.

Answers to Exercise 8.5

1 − 2
1. (a) fx = 3 ( x − ) 2 − 2 (b) fx = − 3x 2 ( x + ) 1
′
3
()
′
() 2x
4
dy 15
(
2
2. (a) = 32xx + ) 1
dx
dy − 7
3
(b) = − ( 63z + 8z − 3 )( z + 4z − 2 3z − ) 3
2
dz
152
Mathematics for Advanced Secondary Schools

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ADVANCED MATH F.5 TG CHAPTERS.indd 152