Revision P1-P2
3
fix
x
Fix Limo
IiEEE
EE
3
e a
4
ex g 11
5 4
ex y 3 94 15
ex y 3 91 3
, Chapter 6: Differentiation
The chain rule
9 3 3 2
dy 0
y = [f (x)] )
n
dx
= n [f (x)]
n¡1
¢ (x)
+ f
Another form of the chain rule
dy dy du
= £
dx du dx
where y is a function of u and u is a function of x.
Example 1: Differentiate 3
24 3 45
¡ ¢4 6x 3 45
11 4
2
(a) y = 3x + 5
13 128 2 813
8 12 8
1 4 4
4
(b) y = 4 (2 + 8x)
q
3
(c) y = (2x3 ¡ 7x)
5
2 7 7512
6 7 2
3
7 312
12
dx dy 1
Note If the subject of the expression is x first find and use =
dy dx dx
( )
dy
(d) x = y 3 + y
dg 3y 1
Eg
3
fix
x
Fix Limo
IiEEE
EE
3
e a
4
ex g 11
5 4
ex y 3 94 15
ex y 3 91 3
, Chapter 6: Differentiation
The chain rule
9 3 3 2
dy 0
y = [f (x)] )
n
dx
= n [f (x)]
n¡1
¢ (x)
+ f
Another form of the chain rule
dy dy du
= £
dx du dx
where y is a function of u and u is a function of x.
Example 1: Differentiate 3
24 3 45
¡ ¢4 6x 3 45
11 4
2
(a) y = 3x + 5
13 128 2 813
8 12 8
1 4 4
4
(b) y = 4 (2 + 8x)
q
3
(c) y = (2x3 ¡ 7x)
5
2 7 7512
6 7 2
3
7 312
12
dx dy 1
Note If the subject of the expression is x first find and use =
dy dx dx
( )
dy
(d) x = y 3 + y
dg 3y 1
Eg
