Bài tập Toán DIFFERENTIATION 04

Created by T. Madas
Question 8
Carry out the following differentiations.

a)

d
4 y3 + 6 y + 2
dy

b)

1
d 2

 7t − 4t 2 
dt 


c)

d
ax 2 + bx + c
dx

d)

d 1 2 1
 z − 
dz  4
z

d 1 2 1 1
1
 z − = z+ 2
dz  4
z 2
z

e)

d  1 54 k 
 w + 2
dw  4
w 

d  1 54 k  1 − 15 2k
 w + 2= w − 3
dw  4
w  5
w

(

(

)

d
4 y 3 + 6 y + 2 = 12 y 2 + 6
dy

(

)

1
d 2
−1

 7t − 4t 2  = 14t − 2t 2
dt 


)

d
ax 2 + bx + c = 2ax + b
dx

(

Created by T. Madas

)


Created by T. Madas
Question 9
a) If A = π x 2 − 20 x , find the rate of change of A with respect to x .
b) If V = x − 2π x3 , find the rate of change of V with respect to x .

c) If P = at 2 − bt , find the rate of change of P with respect to t .
1

d) If W = 6kh 2 − h , find the rate of change of W with respect to h .
2

e) If N = ( at + b ) , find the rate of change of N with respect to t .
dA
dV
dP
dW
−1
= 2π x − 20 ,
= 1 − 6π x 2 ,
= 2at − b ,
= 3kh 2 − 1 ,
dx
dh
dx
dt
dN
= 2a 2t + 2ab
dt

Created by T. Madas


Created by T. Madas

DIFFERENTIATING

INDICES

Created by T. Madas