Page 5 - PRE-U STPM MATHEMATICS (T) TERM 2

Mathematics Term 2 STPM Chapter 2 Differentiation

= lim  2xx + (x) 2 4
x → 0 x
= lim (2x + x)
x → 0
= 2x
1 _ 1
d 1 x + x x
(b) 1 2 = lim  4
dx x x → 0 x
= lim  x – (x + x) 4
x → 0 (x + x)x (x)
2
= lim  –1 4
x → 0 x(x + x)
= – 1
x 2

Example 2

dy
2
If y = 3x + x + 1, find from the first principles.
dx
2
2
dy 3(x + x) + (x + x) + 1 – (3x + x + 1)
Solution: = lim  4
dx x → 0 x
2
2
2
= lim  3x + 6xx + 3(x) + x + x + 1 – 3x – x – 1 4
x → 0 x
2
= lim  6x x + 3(x) + x 4
x → 0 x
= lim [6x + 3 x + 1]
x → 0
= 6x + 1

Exercise 2.1

Find the derivatives of the following functions from the first principles.
3
4
1. y = x 2. y = x 3. y = 5x 2
2
2
4. y = 1 5. y = x + 5x 6. y = x – x + 3
x 2
2
3
7. y = 4x 8. y = 1 9. y = 2x + 3
x 3
10. y = 2x – 3x + 1
2

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02 STPM Math(T) T2.indd 18 02/11/2018 12:43 PM