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

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