Page 43 - Hybrid PBD 2022 Tg 5 - Matematik Tambahan

Matematik Tambahan Tingkatan 5 Bab 2 Pembezaan
5. Bezakan yang berikut terhadap x. SP 2.2.1 TP2
Differentiate the following with respect to x.

(a) –6 (b) –5x
4
(i) 12
(ii) –3x 4 d (–6) = 0 d (–5x ) = –20x 3
4
(iii) –2 dx dx
x 4

(i) d(12) = 0 (iii) –2 = –2x -4
dx x 4 (c) –5x 2 (d)  3x
–4
d(–2x ) = –2(–4)x -4–1 3x 4 (x) 2 1 2

2 

3
dx = 8x –5 d –5 x = 10 x –3 d  3x = d ( 3x )

–
–2
2
= xPenerbitan Pelangi Sdn Bhd. All Rights Reserved.
3
4
(ii) d(–3x ) = –3(4)x 4 – 1 8 dx 3 10 dx x dx 5
x
dx = –12x 3 = x 5 = 3x 3 = –3 3 – 2
2
6. Cari f’(x) bagi setiap fungsi yang berikut. SP 2.2.2 TP2
Find f’(x) for each of the following functions.
4 5 3  x
1 (a) f(x) =  2x (b) f(x) = –2 (c) f(x) = –2
f(x) = x 5 4x 2x
2 f(x) = 4 x – 1 2 f(x) = 5 x 2 x 1 3 1 7
1
–2
f’(x) = (5) x 4  2 4 f(x) = 2x = x 3
2
2 4 1 – 3 2 f‘(x) = 5 x 1 7 4
 
–
5 f‘(x) =  2   x 2 f‘(x) = 2 3 x 3
2
= x 4
2 = – 2 7 4
 x 3 = x 3
6
Tip Penting
dy
f’(x) =
dx
7. Cari nilai terbitan pertama bagi setiap fungsi yang berikut dengan nilai x yang diberi. SP 2.2.2 TP3
Find the value of the first derivative for each of the following functions with the given value of x.

– x 5 8x 3 –1 1
x 6 (a) f(x) = 2 , x = 4 (b) f(x) = 3 x , x = 3 (c) y = (2x) –2 , x = – 4
y = , x = 2
3x 3 –x 5 2 8 3– 1
2
x 6 f(x) = f(x) = x 2 y = –(2x) = –4x 2
3
y = 2 dy
8
3x 3 = x 5 2 = –8x
 
1 f‘(x) = – 1 5 x 3 2 3 dx
3 2 2 1
3 5 3 f’(x) = 8 5 x 3 2 Apabila/When x = – 4
 
1
 
2
dy = (3)x = – x 2 3 2 3 dy = –8 – 1
4
20
dx 3 Apabila/When x = 4 = x 2 dx 4
= x 2 5 3 3 = 2
Apabila/When x = 2 f‘(4) = – (4) 2 Apabila/When x = 3
4
20
3
5
dy = (2 ) = – (2 ) = –10 f’(3) = 3 (3) 2
2
3
dx
= 4 4 = 20 3
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