Bài tập Toán DIFFERENTIATION 03

Created by T. Madas
Question 5
Find f ′ ( x ) for each of the following functions.

f ′ ( x ) = 12 x 2 − 9

a) f ( x ) = 4 x3 − 9 x + 2

b) f ( x ) = 6 x

− 12

f ′ ( x ) = −3 x

+ 2x
5

− 32

+2
3

f ′ ( x ) = 4 x3 + 5 x 2

c) f ( x ) = x 4 + 2 x 2
3

−
d) f ( x ) = 1 x 2 − 4 x 2
2

f ′( x) = x + 6x

1

e) f ( x ) = 1 x 3 + 5 x
2

f ′( x) = 1 x
6

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− 23

− 52

+5


Created by T. Madas
Question 6
Differentiate each of the following functions with respect to x .

a)

f ( x) = 6x

− 32

f ′ ( x ) = −9 x

+ 4x +1

− 52

+4

b) g ( x ) = x 4 − x −1

g ′ ( x ) = 4 x3 + x −2

c) h ( x ) = 9 x 2 − 1 x 4
2

h′ ( x ) = 18 x − 2 x3

1

1

d) p ( x ) = 4 x 2 − 6 x 3 + 1 x
2

(

e) v ( x ) = 8 x + 1
2

)

2

− 14

p′ ( x ) = 2 x

− 12

− 2x

v′ ( x ) = 128 x + 8

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− 32

−1x
8

− 45


Created by T. Madas
Question 7
Carry out the following differentiations.

a)

d
4t 2 − 7t + 5

dt

b)

d  12 2 − 12 
y −3y 
dy 


c)

d
2 z 2 − 3 z −1 + z
dz

d)

d  2
−3 
w −w 2 
dw 


5
d  2
−3 
3 −
 w − w 2  = 2w + 2 w 2
dw 


e)

d
ax 2 − 3 x 2
dx

d
ax 2 − 3 x 2 = 2ax − 6 x
dx

(

(

(

)

d
4t 2 − 7t + 5 = 8t − 7
dt

(

)

)

d  12 2 − 12  1 − 12 1 − 23

y −3y = 2y +3y
dy 


)

d
2 z 2 − 3 z −1 + z = 4 z + 3 z −2 + 1
dz

(

(

Created by T. Madas

)

)