Page 44 - Hybrid PBD 2022 Tg 5 - Matematik Tambahan

Matematik Tambahan Tingkatan 5 Bab 2 Pembezaan
8. Cari terbitan pertama terhadap x bagi setiap fungsi yang berikut.
Find the first derivative with respect to x for each of the following. SP 2.2.2 TP3

(i) dy = d (–x ) – d (3x ) + d (2)
3
2
(i) y = –x – 3x + 2 dx dx dx dx
2
3
2
(x – 2)(3 – 2x) = –3x – 6x
(ii) y =
x 2
(ii) y = 3x – 2x – 6 + 4x
x
Tip Penting 6
= –2x + 7 –
Guna/Use x
y = f(x) = h(x) ± g(x), = –2x + 7 – 6x –1
dy df(x) d dy 6
maka = = h(x) ± g(x) –2
dx dx dx dx = –2 + 6x = –2 + x 2
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2
(a) f(x) = 2x 3  1 – 3  (b) y =  x ( x – x )
x
4
y = x – x 5 2
1
f(x) = x – 6x 2 dy 5 3
3
2 = 1 – x 2
3 dx 2
f’(x) = x – 12x 5
2
2 = 1 –  3
x
2

9. Cari nilai terbitan pertama terhadap x untuk setiap fungsi berikut bagi nilai x yang diberikan.
Find the value of the first derivative with respect to x for each of the following functions with the given value of x. SP 2.2.2 TP3

3
y =  2 – x  2 , x = –2 (a) y = (2x + 3)(1 – x ) , x = –1
3x
2
4
4
1 y = 2x – 2x + 3 – 3x 3
y = [4 – 4x + x ] 3x 2
2
16 Tip Penting
2
2
1 1 1 y = x – x + x – x
–1
2
–2
= – x + x 2 Ungkapkan dalam sebutan 3 3
4 4 16 berasingan dahulu.
1
4
dy 1 1 Express in separate terms first. dy = –2 – x – – 1
= – + x dx 3x 2 3 x 3
dx 4 8 dy –2 4
dy 1 1 Apabila x = –1, = + + 1 – 1
Apabila/When x = –2, = – + (–2) dx 3 3
dx 4 8 When 2
1 =
= – 3
2
1
1

4x 2 – 1  1 (c) y = x 3 –  , x =
3
3
2
(b) f(x) = x , x = – 2x 3
7x 2 2 3 1
3
4 1 y = x 9 – + 

f(x) = x 2 –  x 4x 2
7 x 1
8 4 y = 9x – 3x + x
3
2
= x – 4

7 7 dy 1
8 = 27x – 6x +
2
f‘(x) = dx 4
7 1 dy 1 1 1
Apabila x = , = 27   – 6   + 4
3 dx
3
9
When
= 1 1
4
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02 Hybrid PBD Mate Tamb Tg5.indd 23 09/11/2021 9:24 AM