Bài tập Toán DIFFERENTIATION 02

Created by T. Madas
Question 2
Evaluate the following.

a)

d
4 x3
dx

d
4 x3 = 12 x 2
dx

b)

d
7 x5
dx

d
7 x5 = 35 x 4
dx

c)

d
4 x 2 + 3x 4
dx

d)

d 2
x + 7x + 5
dx

e)

d  12
−2 
 8x + 2 x 
dx 


( )

( )

( )

( )
(

(

d
4 x 2 + 3 x 4 = 8 x + 12 x3
dx

(

)
)

)

d 2
x + 7x + 5 = 2x + 7
dx

(

)

d  12
−1
−2 
−3
 8x + 2 x  = 4 x 2 − 4 x
dx 


Created by T. Madas


Created by T. Madas
Question 3
Differentiate the following expressions with respect to x
dy
= 2 x − 24 x5
dx

a) y = x 2 − 4 x 6

3

b) y = 5 x3 − 6 x 2

1
dy
= 15 x 2 − 9 x 2
dx

c) y = 9 x −3 + 7 x −2

dy
= −27 x −4 − 14 x −3
dx

d) y = 5 − 5 x −1

dy
= 5 x −2
dx

e) y = 7 x + x

dy
1 −1
=7+ x 2
dx

2

Created by T. Madas


Created by T. Madas
Question 4
Differentiate the following expressions with respect to x

a) y = x6 − 7 x 2

5

dy
= 6 x5 − 14 x
dx

b) y = 1 − 6 x 2

3
dy
= 15 x 2
dx

c) y = 2 x + 8 x −2

dy
= 2 + 16 x −3
dx

d) y = ( 2 x − 1)( 4 x + 3)

dy
= 16 x + 2
dx

e) y = 4 x 3 ( 2 − 3x )

dy
= 24 x 2 − 48 x3
dx

Created by T. Madas