Page 159 - ADVANCED MATH F.5

Form Five Form Five

(c) dy = 18x (3x − 2 (d) dy = ( xx + ) 5 − 1 2
2
2
dx ) 4 dx
1
3. (a) ft ′ () = (t − 3 )(t − 2 6t + ) 7 − 2
FOR ONLINE READING ONLY
(b) ft ′ ( ) = − 21 (3 t− )
20
3 − 3
(c) gz ′ () = z 2 (3 z 3 )
−
2
2
3
−
2 ⎛ 1 ⎞⎛ 1 ⎞
5
(d) z′ = ⎜ x + ⎟⎜ 1− 2 ⎟
5 ⎝ x ⎠⎝ x ⎠
(e) y′ = 2.9 t − ( 3 t ) ⎜ 1.9 ⎛ 3t − 2 1 ⎞ ⎟
⎝ 2 t ⎠

8t + 3 9t − 2 5
5. (a) f ()t ′ = − 4 (b) f ′ ( 1) 0.06189−=
3 3 ( 2t + 4 3t − 3 5t + ) 6

4
r + 1 1
6. r′ = 8. x′ = 2
r 2 r − 1 3 ⎛ 2 ⎞ 3
4
3u 2 ⎜ 1− ⎟
15 ⎝ u ⎠
4
7. θ 10 (4 2θ′ = − − ) 9. 16

Differentiation of implicit functions

Teaching steps
1. Use Think-Ink-Pair-Share strategy to recognize an implicit
function. Assist students to write an implicit function in terms
of both dependent and independent variables.

2. Guide students through discussions to use the product rule and
chain rule to deduce the implicit differentiation formula of the
d dy
n
form, ( xy n ) = nxy n− 1 + mx m− 1 y . Allow students to
m
m
dx dx
153
Mathematics for Advanced Secondary Schools

30/06/2024 18:02:38
ADVANCED MATH F.5 TG CHAPTERS.indd 153 30/06/2024 18:02:38
ADVANCED MATH F.5 TG CHAPTERS.indd 153