Differentiation practice i - MadAsMaths

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DIFFERENTIATION PRACTICE

Created by T. Madas

Created by T. Madas

THE OPERATION OF

DIFFERENTIATION

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Question 1 Evaluate the following.

( ) a) d 5x6 dx

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( ) d 5x6 = 30x5

dx

b)

d dx

2

x

3 2

d dx

2

x

3 2

=

3x

1 2

( ) c) d 6x4 - x3 dx

( ) d 6x4 - x3 = 24x3 - 3x2

dx

( ) d) d 3x2 + 5x +1 dx

( ) d 3x2 + 5x +1 = 6x + 5

dx

e)

d dx

4x

1 2

-

2x

-

7

d dx

1

4x2

-

2x

-

7

=

2

x

-

1 2

-

2

Created by T. Madas

Question 2 Evaluate the following.

( ) a) d 4x3 dx

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( ) d 4x3 = 12x2

dx

( ) b) d 7x5 dx

( ) d 7x5 = 35x4

dx

( ) c) d 4x2 + 3x4 dx

( ) d 4x2 + 3x4 = 8x +12x3

dx

( ) d) d x2 + 7x + 5 dx

( ) d x2 + 7x + 5 = 2x + 7

dx

e)

d dx

8

x

1 2

+

2 x -2

d dx

8x

1 2

+

2x-2

=

4

x-

1 2

-

4x-3

Created by T. Madas

Created by T. Madas

Question 3 Differentiate the following expressions with respect to x

a) y = x2 - 4x6

dy = 2x - 24x5 dx

b)

y

=

5x3

-

6x

3 2

dy

= 15x2

1

- 9x2

dx

c) y = 9x-3 + 7x-2

dy = -27x-4 -14x-3 dx

d) y = 5 - 5x-1

dy = 5x-2 dx

e) y = 7x + x

dy

=

7

+

1

x-

1 2

dx 2

Created by T. Madas

Created by T. Madas

Question 4 Differentiate the following expressions with respect to x

a) y = x6 - 7x2

dy = 6x5 -14x dx

5

b) y = 1- 6x 2

dy

3

= 15x 2

dx

c) y = 2x + 8x-2

dy = 2 +16x-3 dx

d) y = (2x -1)(4x + 3)

dy = 16x + 2 dx

e) y = 4x3 (2 - 3x)

dy = 24x2 - 48x3 dx

Created by T. Madas

Created by T. Madas

Question 5

Find f ( x) for each of the following functions.

a) f ( x) = 4x3 - 9x + 2

f ( x) = 12x2 - 9

b)

f

(

x)

=

6

x-

1 2

+

2x

f

(

x)

=

-3x-

3 2

+

2

c)

f

(x)

=

x4

+

5

2x2

f

(

x

)

=

4

x3

+

5

x

3 2

d)

f

(x)

=

1 2

x2

-

4x

-

3 2

e)

f

(x)

=

1 2

1

x3

+

5x

f

(

x)

=

x

+

6

x-

5 2

f

(

x)

=

1 6

x-

2 3

+

5

Created by T. Madas

Created by T. Madas

Question 6 Differentiate each of the following functions with respect to x .

a)

f

(x)

=

6x

-

3 2

+

4x

+ 1

f

(

x)

=

-9

x-

5 2

+

4

b) g ( x) = x4 - x-1

g( x) = 4x3 + x-2

c)

h

(

x

)

=

9x2

-

1 2

x

4

d)

p

(

x)

=

1

4x2

-

1

6x3

+

1 2

x-

1 4

( ) e)

v(x) =

8x

+

1 2

2

h( x) = 18x - 2x3

p(

x)

=

2x

-

1 2

-

2

x-

2 3

-

1 8

x-

5 4

v( x) = 128x + 8

Created by T. Madas

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