Differentiation dominoes 3 – chain, product and quotient rules
Cut along the dashed lines to create 24 domino cards. Match the dominoes by differentiating the
expression on the right hand side with respect to x (a, b, c and d are constants), giving your answer
in its simplest form. The dominoes form one continuous loop.
3x 2
6 2x
1 2
x
2
15 2
x
4
36 x 3
(x a)3
4x 1
a(b x)3
10
x
3
5
2
(x 2)2
3x 2
7x x 2
x
20 4
x
b
2x 4
3x 2
x 1
3 ax bx 2
20 x 4
2ax 3
0
–1
x b
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3x 4
5x 3
x2
5 3
x
4
1 6
x
a
2
x
5 2
x
3
b 4
x
3
4 3
cx
3
a
4 5
x
b
3ab 2
6abx 3ax 2
8ax
2
5
21(2 x 3)
5
x a
2
2x 7
3 2
x
2
9(2 x 1)
20320
c 4
x
3
2 3
x
d
4x3 x
2x 1
6 2
x
d
0.5( x 3 8)
x 2
2x 4
(x 2 1)(x 3)
x 1
x
6ax 3a 2
4 x2
(3x 2 2x 1)2
1
3
x3
bx c
3x
36 x 2
7 3 x ax 2
( x 1)( x 2)( x 3)
4 3
bx
3
2bx a
7
45
6x 5
ax 7.3
a
6 5
x
a
8
x
15
3x 2
ab 6
8x 1
a(0.5 2 x)(2 x 0.5)
(x 2
6 x 8)(x 5)
x 4
(x 2
x 6)(4 x)
x 3
(x 2)3 (x 1)3
(2 x)3
(x 5)3
Page 1 of 2
Differentiation dominoes 3 – chain, product and quotient rules
These expressions use a mixture of basic differentiation and the chain, product and quotient rules.
Some expressions require polynomial division to find the answer in its simplest form.
Answers (reading down the page)
3x 2
2
x
20 4
x
b
x
2
5
x
x
7 3 x ax 2
2
5
21(2 x 3)
(x 2
x3
6 2x
a
2x 4
0.5( x 3 8)
x 2
x b
x 1
(x a)3
2ax 3
6ax 3a 2
4 3
cx
3
a
4 5
x
b
6abx 3ax 2
c 4
x
3
6 5
x
a
2 3
x
d
2x 7
© www.teachitmaths.co.uk 2013
(x 2
1 2
x
2
1 6
x
a
15 2
x
4
5
2
36 x 3
(x 2)3 (x 1)3
36 x 2
6x 5
20320
5 2
x
3
5
x a
2
(x 2)2
(3x 2 2x 1)2
2x 4
6 x 8)(x 5)
x 4
3 2
x
2
b 4
x
3
7x x 2
x
5 3
x
4
10
x
3
bx c
3 ax bx 2
3x
–1
a(0.5 2 x)(2 x 0.5)
8ax
x 6)(4 x)
x 3
2bx a
a(b x)3
(x 5)3
ax 7.3
4 3
bx
3
4x3 x
2x 1
6 2
x
d
4x 1
3ab 2
(2 x)3
(x 2 1)(x 3)
x 1
3x 2
3x 2
2
1
3
0
1
3
9(2 x 1)
ab 6
8x 1
20 x 4
3x 4
5x 3
x2
4 x2
( x 1)( x 2)( x 3)
Page 2 of 2