RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 28. Differentiation

Subject: Maths - Class 11th

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Chapter Exercises

Exercise 28A
Exercise 28B
Exercise 28C
Exercise 28D
Exercise 28E

Exercise 28A

1

Differentiate the following functions:

(i) x-3


(ii) 
2

Differentiate the following functions:

(i)


(ii)


(iii)


3

Differentiate the following functions:

(i) 3x-5


(ii)


(iii)


4

Differentiate the following functions:

(i) 6x5 + 4x3 – 3x2 + 2x – 7


(ii)


(iii) ax3 + bx2 + cx + d, where a, b, c, d are constants
5

Differentiate the following functions:

(i)


(ii)


6

Differentiate the following functions:

(i)


(ii) -5 tan x + 4 tan x cos x – 3 cot x sec x + 2sec x – 13
7

Differentiate the following functions:

(i) (2x + 3) (3x – 5)


(ii) x(1 + x)3


(iii)


(iv)


(v)


(vi) (2x2 + 5x – 1) (x – 3)
8

Differentiate the following functions:

(i)


(ii)


(iii)


(iv)


(v)


(vi)


9

Differentiate the following functions:

(i) If y = 6x5 – 4x4 – 2x2 + 5x – 9, find at x = -1.


(ii) If y = (sin x + tan x), find at .


(iii) If , find at .
10

If , show that .
11

If , prove that .
12

If , find .
13

, find

Exercise 28B

1

Find the derivation of each of the following from the first principle:

(ax + b)
2

Find the derivation of each of the following from the first principle:
3

Find the derivation of each of the following from the first principle:

3x2 + 2x – 5
4

Find the derivation of each of the following from the first principle:

x3 – 2x2 + x + 3
5

Find the derivation of each of the following from the first principle:

x8
6

Find the derivation of each of the following from the first principle:
7

Find the derivation of each of the following from the first principle:
8

Find the derivation of each of the following from the first principle:
9

Find the derivation of each of the following from the first principle:
10

Find the derivation of each of the following from the first principle:
11

Find the derivation of each of the following from the first principle:
12

Find the derivation of each of the following from the first principle:
13

Find the derivation of each of the following from the first principle:
14

Find the derivation of each of the following from the first principle:
15

Find the derivation of each of the following from the first principle:
16

Find the derivation of each of the following from the first principle:
17

Find the derivation of each of the following from the first principle:
18

Find the derivation of each of the following from the first principle:
19

Find the derivation of each of the following from the first principle:

tan2x
20

Find the derivation of each of the following from the first principle:

sin (2x + 3)
21

Find the derivation of each of the following from the first principle:

tan (3x + 1)

Exercise 28C

1

Differentiate:

X2 sin x
2

Differentiate:

ex cos x
3

Differentiate:

ex cot x
4

Differentiate:

xn cot x
5

Differentiate:

x3 sec x
6

Differentiate:

(x2 + 3x + 1) sin x
7

Differentiate:

x4 tan x
8

Differentiate:

(3x – 5) (4x2 – 3 + ex)
9

Differentiate:

(x2 – 4x + 5) (x3 – 2)
10

Differentiate:

(x2 + 2x – 3) (x2 + 7x + 5)
11

Differentiate:

(tan x + sec x) (cot x + cosec x)
12

Differentiate:

(x3 cos x – 2x tan x)

Exercise 28D

1

Differentiate
2

Differentiate
3

Differentiate
4

Differentiate
5

Differentiate
6

Differentiate
7

Differentiate
8

Differentiate
9

Differentiate
10

Differentiate
11

Differentiate
12

Differentiate
13

Differentiate
14

Differentiate
15

Differentiate
16

Differentiate
17

Differentiate
18

Differentiate
19

Differentiate
20

Differentiate
21

Differentiate
22

Differentiate
23

Differentiate
24

Differentiate
25

Differentiate
26

(i) cotx


(ii) secx

Exercise 28E

1

Differentiate the following with respect to x:

sin 4x
2

Differentiate the following with respect to x:

cos 5x
3

Differentiate the following with respect to x:

tan3x
4

Differentiate the following with respect to x:

cos x3
5

Differentiate the following with respect to x:

cot2x
6

Differentiate the following with respect to x:

tan3x
7

Differentiate the following with respect to x:

tan
8

Differentiate the following with respect to x:
9

Differentiate the following with respect to x:
10

Differentiate the following with respect to x:
11

Differentiate the following with respect to x:

(5 + 7x)6
12

Differentiate the following with respect to x:

(3 - 4x)5
13

Differentiate the following with respect to x:

(3x2 - x + 1)4
14

Differentiate the following with respect to x:

(ax2 + bx + c)
15

Differentiate the following with respect to x:
16

Differentiate the following with respect to x:

sin2 (2x + 3)
17

Differentiate the following with respect to x:

cos2(x3)
18

Differentiate the following with respect to x:
19

Differentiate the following with respect to x:
20

Differentiate the following with respect to x:
21

Differentiate the following with respect to x:

cos 3x sin 5x
22

Differentiate the following with respect to x:

sin x sin 2x
23

Differentiate w.r.t x:

24

Differentiate w.r.t x: e2x sin 3x
25

Differentiate w.r.t x: e3x cos 2x
26

Differentiate w.r.t x: e-5x cot 4x
27

Differentiate w.r.t x: cos (x3 . ex)
28

Differentiate w.r.t x: e(xsinx+cosx)
29

Differentiate w.r.t x:

30

Differentiate w.r.t x:

31

Differentiate w.r.t x:

32

Differentiate w.r.t x:

33

Differentiate w.r.t x:

34

Differentiate w.r.t x:

35

Differentiate w.r.t x:

36

Find ,When
37

Find ,When = ex log (sin 2x)
38

Find ,When

39

Find ,When
40

Find ,When
41

If , show that

42

If , show that .
43

, prove that

44

, show that