Differentiation

Higher Mathematics

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Differentiate24 3 7x x

8 3x

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Differentiate

3 26 3 9x x x

x

3 26 3 9x x x

x x x x

2 16 3 9x x x

Split up

Straight line form

22 6 9x x Differentiate

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Differentiate

3 1

2 22 5x x

1 3

2 23 12 2

2 5x x

1 3

2 25

23x x

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Differentiate2

3 1xx

1 1

2 23 2 1x x

Straight line form

Differentiate

1 3

2 21

2

32

2x x

1 3

2 23

2x x

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Differentiate (3 5)( 2)x x

23 6 5 10x x x Multiply out

Differentiate 6 1x

23 10x x

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Differentiate 2 8003 r

r

2 13 800r r Straight line form

Differentiate26 ( 1)800r r

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Differentiate2( 2 )x x x

multiply out3 22x x

differentiate23 4x x

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Differentiate3

1 1

x x

1 3x x Straight line form

Differentiate2 4( 3)x x

2 43x x

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Differentiate 2x x x

1

22x x xStraight line form

multiply out

Differentiate

5 3

2 2x x3 1

2 25 3

2 2x x

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Differentiate 2 4x x

multiply out

Simplify

4 8 2x x x

Differentiate

6 8x x

Straight line form

1

26 8x x 1

23 1x

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Differentiate5( 2)x

Chain rule45( 2) 1x

45( 2)x Simplify

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Differentiate3(5 1)x

Chain Rule23(5 1) 5x

215(5 1)x Simplify

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Differentiate2 4(5 3 2)x x

Chain Rule 2 34(5 3 2) 10 3x x x

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Differentiate

5

2(7 1)x

Chain Rule

Simplify

3

25

2(7 1) 7x

3

235

2(7 1)x

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Differentiate

1

2(2 5)x

Chain Rule

Simplify

3

21

2(2 5) 2x

3

2(2 5)x

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Differentiate 3 1x

Chain Rule

Simplify

Straight line form 1

23 1x

1

21

23 1 3x

1

23

23 1x

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Differentiate 42

5

3x

Chain Rule

Simplify

Straight line form2 45( 3)x

2 520( 3) 2x x

2 540 ( 3)x x

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Differentiate1

2 1x

Chain Rule

Simplify

Straight line form

1

2(2 1)x

3

21

2(2 1) 2x

3

2(2 1)x

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Differentiate2

2cos sin3

x x

22sin cos

3x x

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Differentiate 3cos x

3sin x

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Differentiate cos 4 2sin 2x x

4sin 4 4cos 2x x

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Differentiate4cos x

34cos sinx x

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Differentiate sin x

Chain Rule

Simplify

Straight line form

1

2(sin )x1

21

2(sin ) cosx x

1

21

2cos (sin )x x

1

2

cos

sin

x

x

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Differentiate sin(3 2 )x

Chain Rule

Simplify

cos(3 2 ) ( 2)x

2cos(3 2 )x

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Differentiatecos5

2

x

Chain Rule

Simplify

1

2cos5xStraight line form

1

2sin 5 5x

5

2sin 5x

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Differentiate ( ) cos(2 ) 3sin(4 )f x x x

( ) 2sin(2 ) 12cos(4 )f x x x

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Differentiate2 43200

( )A x xx

Chain Rule

Simplify

Straight line form2 1( ) 43200A x x x

2( ) 2 43200A x x x

2

43200( ) 2A x x

x

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Differentiate 2

2( )f x x

x

Differentiate

Straight line form

122( ) 2f x x x

1321

2( ) 4f x x x

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Differentiate 3 22 7 4 4y x x x

26 14 4y x x

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Differentiate 62siny x

Chain Rule

Simplify

62 cos 1

dyx

dx

62 cos

dyx

dx

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Differentiate3

(8 )4

A a a

multiply out

Differentiate

236

4A a a

36

2A a

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Differentiate

13 2( ) (8 )f x x

Chain Rule

Simplify

13 221

2( ) (8 ) ( 2 )f x x x

12 3 2( ) (8 )f x x x

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Differentiate16

, 0y x xx

Differentiate

Straight line form1

216y x x

3

21 8dy

xdx

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Differentiate 23 3 16( )

2A x x

x

Straight line form

Multiply out23 3 3 3 16

( )2 2

A x xx

Differentiate

2 13 3( ) 24 3

2A x x x

2( ) 3 3 24 3A x x x

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Differentiate 1

2( ) 5 4f x x

Chain Rule

Simplify

1

21

2( ) 5 4 5f x x

1

25

2( ) 5 4f x x

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Differentiate 216( ) 240

3A x x x

32( ) 240

3A x x

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Differentiate 2( ) 3 (2 1)f x x x

Multiply out

Differentiate

3 2( ) 6 3f x x x

2( ) 18 6f x x x

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Differentiate2 2( ) cos sinf x x x

( ) 2 cos sin 2sin cosf x x x x x Chain Rule

Simplify ( ) 4 cos sinf x x x

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