Page 45 - Hybrid PBD 2022 Tg 5 - Matematik Tambahan

Matematik Tambahan Tingkatan 5 Bab 2 Pembezaan
10. Tentukan terbitan pertama bagi fungsi gubahan yang berikut. SP 2.2.3 TP3
Determine the first derivative for the following composite functions.

i
(i) y = (2 – 3x) 3 (ii) f(x) = –2
2 3
Katakan u = 2 – 3x Tip Penting 3(x – x )
2
2 –3
Let du = –3 f(x) = – (x – x )
dx Gunakan petua rantai 3
Maka y = u 3 Use chain rule Katakan u = x – x 2
dy
du
dy
Therefore dx = du × dx Let du = 1 – 2x
dy = 3u 2 dx
2
du f(x) = – u –3
dy = dy × du df(x) 3
dx du dx y = (2 – 3x) 3 du = 2u –4
dxAll Rights Reserved.
d
2
= 3u (–3) dy = 3(2 – 3x) 3 – 1 dx (2 – 3x) f(x) = – (x – x )
2
dx
2 –3
= –9u 3 = 3(2 – 3x) (–3) df(x) = df(x) × du df(x) 3 2 d
2
= –9(2 – 3x) 2 = –9(2 – 3x) 2 dx 2 du dx dx = – (–3)(x – x ) dx (x – x )
2 –3 – 1
2
3
= (1 – 2x) 2 –4
u 4 = 2(x – x ) (1 – 2x)
2(1 – 2x) = 2(1 – 2x)
= (x – x )
2 4
(x – x )
2 4
1 1
(a) f(x) = (b) y = (4x – 6x )
2 4
 2 – 1 5 2 1

x
2 4
f(x) = (2 – x ) y = (4x – 6x )
2
–1 –5
Penerbitan Pelangi Sdn Bhd.
1

  
f‘(x) = –5 2 – 1 –6 1 2 dy = (4)(4x – 6x ) (4 – 12x)
2 3
x
x
–5 2 2 3
= = 2(4 – 12x)(4x – 6x )


x 2 – 1 6 = 8(1 – 3x)(4x – 6x )
2 3
2
x
–4
2 3
(c) y = (1 – x ) (d) f(x) = 
6
x + 3
1 – 1
y = (1 – x ) f(x) = –4(x + 3) 2
2 3
6 1 3
 
dy = (3)(1 – x ) (–2x) f‘(x) = –4 – 2 (x + 3) – 2
1
2 2
dx 6 2
1 =
= – x(1 – x )  3
(x + 3)
2 2
3
dy
11. Cari nilai bagi pada setiap nilai x yang diberi berikut. SP 2.2.3 TP4
dx
dy
Find the value of for each of the following given value of x.
dx

2
2 (a) y = 3 2x – 2 , x = 3
y = , x = –1 4
 3 2 1 2
3 – x
4
y = 2(3 – x) – 1 2 y = (2x – 2)
dy 1 3 dy 3 1 2 – 1
 
–
= 2 – (3 – x) (–1) =   (2x – 2) (4x)
2
2
dx 2 dx 4 2
3x
= 1 = 
2
(3 – x)
 3 2 2x – 2
dy 1 x = 3, dy = 9

x = –1, = dx 2 16
(4)
dx  3
1 = 9
= 8
8
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02 Hybrid PBD Mate Tamb Tg5.indd 24 09/11/2021 9:24 AM