RS Aggarwal Solutions for Class 12 Chapter 10: Differentiation

In this chapter, students primarily obtain a brief idea about the rules to be followed in solving the exercise wise problems. Derivatives of logarithmic, exponential, inverse trigonometric functions are the main concepts which are discussed under this chapter. The well experienced faculty at BYJU’S prepare solutions with the aim of helping students score well in the class 12 exams. The solutions are designed in an interactive manner to enhance their interest in the subject. To perform well in the class 12 exam, students can make use of RS Aggarwal Solutions for Class 12 Chapter 10 Differentiation PDF from the links given here.

RS Aggarwal Solutions for Class 12 Chapter 10: Differentiation Download PDF

 

rs aggarwal solution class 12 maths chapter 10 ex a 1
rs aggarwal solution class 12 maths chapter 10 ex a 2
rs aggarwal solution class 12 maths chapter 10 ex a 3
rs aggarwal solution class 12 maths chapter 10 ex a 4
rs aggarwal solution class 12 maths chapter 10 ex a 5
rs aggarwal solution class 12 maths chapter 10 ex a 6
rs aggarwal solution class 12 maths chapter 10 ex a 7

rs aggarwal solution class 12 maths chapter 10 ex b 01
rs aggarwal solution class 12 maths chapter 10 ex b 02
rs aggarwal solution class 12 maths chapter 10 ex b 03
rs aggarwal solution class 12 maths chapter 10 ex b 04
rs aggarwal solution class 12 maths chapter 10 ex b 05
rs aggarwal solution class 12 maths chapter 10 ex b 06
rs aggarwal solution class 12 maths chapter 10 ex b 07
rs aggarwal solution class 12 maths chapter 10 ex b 08
rs aggarwal solution class 12 maths chapter 10 ex b 09
rs aggarwal solution class 12 maths chapter 10 ex b 10
rs aggarwal solution class 12 maths chapter 10 ex b 11

rs aggarwal solution class 12 maths chapter 10 ex c 1
rs aggarwal solution class 12 maths chapter 10 ex c 2
rs aggarwal solution class 12 maths chapter 10 ex c 3
rs aggarwal solution class 12 maths chapter 10 ex c 4
rs aggarwal solution class 12 maths chapter 10 ex c 5

rs aggarwal solution class 12 maths chapter 10 ex d 01
rs aggarwal solution class 12 maths chapter 10 ex d 02
rs aggarwal solution class 12 maths chapter 10 ex d 03
rs aggarwal solution class 12 maths chapter 10 ex d 04
rs aggarwal solution class 12 maths chapter 10 ex d 05
rs aggarwal solution class 12 maths chapter 10 ex d 06
rs aggarwal solution class 12 maths chapter 10 ex d 07
rs aggarwal solution class 12 maths chapter 10 ex d 08
rs aggarwal solution class 12 maths chapter 10 ex d 09
rs aggarwal solution class 12 maths chapter 10 ex d 10
rs aggarwal solution class 12 maths chapter 10 ex d 11
rs aggarwal solution class 12 maths chapter 10 ex d 12
rs aggarwal solution class 12 maths chapter 10 ex d 13
rs aggarwal solution class 12 maths chapter 10 ex d 14
rs aggarwal solution class 12 maths chapter 10 ex d 15
rs aggarwal solution class 12 maths chapter 10 ex d 16
rs aggarwal solution class 12 maths chapter 10 ex d 17
rs aggarwal solution class 12 maths chapter 10 ex d 18
rs aggarwal solution class 12 maths chapter 10 ex d 19
rs aggarwal solution class 12 maths chapter 10 ex d 20
rs aggarwal solution class 12 maths chapter 10 ex d 21
rs aggarwal solution class 12 maths chapter 10 ex d 22
rs aggarwal solution class 12 maths chapter 10 ex d 23
rs aggarwal solution class 12 maths chapter 10 ex d 24

rs aggarwal solution class 12 maths chapter 10 ex e 01
rs aggarwal solution class 12 maths chapter 10 ex e 02
rs aggarwal solution class 12 maths chapter 10 ex e 03
rs aggarwal solution class 12 maths chapter 10 ex e 04
rs aggarwal solution class 12 maths chapter 10 ex e 05
rs aggarwal solution class 12 maths chapter 10 ex e 06
rs aggarwal solution class 12 maths chapter 10 ex e 07
rs aggarwal solution class 12 maths chapter 10 ex e 08
rs aggarwal solution class 12 maths chapter 10 ex e 09
rs aggarwal solution class 12 maths chapter 10 ex e 10
rs aggarwal solution class 12 maths chapter 10 ex e 11

rs aggarwal solution class 12 maths chapter 10 ex f 01
rs aggarwal solution class 12 maths chapter 10 ex f 02
rs aggarwal solution class 12 maths chapter 10 ex f 03
rs aggarwal solution class 12 maths chapter 10 ex f 04
rs aggarwal solution class 12 maths chapter 10 ex f 05
rs aggarwal solution class 12 maths chapter 10 ex f 06
rs aggarwal solution class 12 maths chapter 10 ex f 07
rs aggarwal solution class 12 maths chapter 10 ex f 08
rs aggarwal solution class 12 maths chapter 10 ex f 09
rs aggarwal solution class 12 maths chapter 10 ex f 10
rs aggarwal solution class 12 maths chapter 10 ex f 11
rs aggarwal solution class 12 maths chapter 10 ex f 12
rs aggarwal solution class 12 maths chapter 10 ex f 13
rs aggarwal solution class 12 maths chapter 10 ex f 14
rs aggarwal solution class 12 maths chapter 10 ex f 15
rs aggarwal solution class 12 maths chapter 10 ex f 16
rs aggarwal solution class 12 maths chapter 10 ex f 17
rs aggarwal solution class 12 maths chapter 10 ex f 18
rs aggarwal solution class 12 maths chapter 10 ex f 19
rs aggarwal solution class 12 maths chapter 10 ex f 20
rs aggarwal solution class 12 maths chapter 10 ex f 21
rs aggarwal solution class 12 maths chapter 10 ex f 22
rs aggarwal solution class 12 maths chapter 10 ex f 23
rs aggarwal solution class 12 maths chapter 10 ex f 24
rs aggarwal solution class 12 maths chapter 10 ex f 25
rs aggarwal solution class 12 maths chapter 10 ex f 26
rs aggarwal solution class 12 maths chapter 10 ex f 27
rs aggarwal solution class 12 maths chapter 10 ex f 28
rs aggarwal solution class 12 maths chapter 10 ex f 29
rs aggarwal solution class 12 maths chapter 10 ex f 30
rs aggarwal solution class 12 maths chapter 10 ex f 31
rs aggarwal solution class 12 maths chapter 10 ex f 32

rs aggarwal solution class 12 maths chapter 10 ex g 1
rs aggarwal solution class 12 maths chapter 10 ex g 2
rs aggarwal solution class 12 maths chapter 10 ex g 3
rs aggarwal solution class 12 maths chapter 10 ex g 4

rs aggarwal solution class 12 maths chapter 10 ex h 1
rs aggarwal solution class 12 maths chapter 10 ex h 2
rs aggarwal solution class 12 maths chapter 10 ex h 3
rs aggarwal solution class 12 maths chapter 10 ex h 4
rs aggarwal solution class 12 maths chapter 10 ex h 5
rs aggarwal solution class 12 maths chapter 10 ex h 6

rs aggarwal solution class 12 maths chapter 10 ex i 1
rs aggarwal solution class 12 maths chapter 10 ex i 2
rs aggarwal solution class 12 maths chapter 10 ex i 3
rs aggarwal solution class 12 maths chapter 10 ex i 4
rs aggarwal solution class 12 maths chapter 10 ex i 5
rs aggarwal solution class 12 maths chapter 10 ex i 6
rs aggarwal solution class 12 maths chapter 10 ex i 7
rs aggarwal solution class 12 maths chapter 10 ex i 8
rs aggarwal solution class 12 maths chapter 10 ex i 9

rs aggarwal solution class 12 maths chapter 10 ex j 01
rs aggarwal solution class 12 maths chapter 10 ex j 02
rs aggarwal solution class 12 maths chapter 10 ex j 03
rs aggarwal solution class 12 maths chapter 10 ex j 04
rs aggarwal solution class 12 maths chapter 10 ex j 05
rs aggarwal solution class 12 maths chapter 10 ex j 06
rs aggarwal solution class 12 maths chapter 10 ex j 07
rs aggarwal solution class 12 maths chapter 10 ex j 08
rs aggarwal solution class 12 maths chapter 10 ex j 09
rs aggarwal solution class 12 maths chapter 10 ex j 10
rs aggarwal solution class 12 maths chapter 10 ex j 11
rs aggarwal solution class 12 maths chapter 10 ex j 12

 

Exercises of RS Aggarwal Solutions Class 12 Maths Chapter 10 – Differentiation

Exercise 10A Solutions

Exercise 10B Solutions

Exercise 10C Solutions

Exercise 10D Solutions

Exercise 10E Solutions

Exercise 10F Solutions

Exercise 10G Solutions

Exercise 10H Solutions

Exercise 10I Solutions

Exercise 10J Solutions

Access RS Aggarwal Solutions for Class 12 Chapter 10: Differentiation

EXERCISE 10A PAGE: 370

Differentiate each of the following w.r.t. x:

1. sin 4x

Solution:

By differentiating both sides w.r.t. x

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 1

2. cos 5x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 2

3. tan 3x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 3

4. cos x3

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 4

5. cot2 x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 5

6. tan3 x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 6

7. cot √x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 7

8. √tan x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 8

9. (5 + 7x) 6

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 9

10. (3 – 4x) 5

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 10

11. (2x2 – 3x + 4) 5

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 11

12. (ax2 + bx + c) 6

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 12

13. 1/ (x2 – 3x + 5) 3

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 13

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 14

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 15

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 16

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 17

16. cos2 x3

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 18

17. sec3 (x2 + 1)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10A Image 19

Exercise 10B PAGE: 379

Differentiate each of the following w.r.t. x:

1. (i) e4x

(ii) e-5x

(iii) ex3

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 1

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 2

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 3

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 4

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 5

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 6

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 7

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 8

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 9

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 10

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 11

4. (i) tan (logx)

(ii) log sec x

(iii) log sin x/2

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 12

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 13

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 14

5. (i) log3x

(ii) 2-x

(iii) 3x+2

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 15

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 16

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 17

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 18

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 19

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 20

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 21

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 22

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 23

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 24

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 25

9. e 2x sin3x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 26

10. e 3x cos2x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 27

11. e-5x cot4x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10B Image 28

Exercise 10C PAGE: 388

Differentiate each of the following w.r.t. x:

1. cos-1 2x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 1

2. tan-1 x2

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 2

3. sec-1 √ x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 3

4. sin-1 x/a

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 4

5. tan-1 (log x)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 5

6. cot-1 (ex)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 6

7. log (tan-1 x)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 7

8. cot-1 x3

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 8

9. sin-1 (cos x)

Solution:

We know that

y = sin-1 (cos x)

It can be written as

y = sin-1 sin [π/2 – x]

So we get

y = π/2 – x

By differentiating both sides w.r.t. x

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 9

10. (1 + x2) tan-1 x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10C Image 10

Exercise 10D page: 402

Differentiate each of the following w.r.t. x:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 1

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 2

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 3

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 4

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 5

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 6

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 7

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 8

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 9

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 10

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 11

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 12

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 13

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 14

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 15

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 16

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 17

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 18

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 19

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 20

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 21

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 22

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 23

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 24

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 25

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 26

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 27

11. cot -1 (cosec x + cot x)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 28

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 29

12. tan-1 (cot x) + cot-1 (tan x)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 30

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 31

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 32

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 33

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 34

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 35

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 36

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 37

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 38

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 39

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 40

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 41

18. sin -1 (3x – 4x3)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 42

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 43

19. sin -1 (1 – 2x2)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 44

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 45

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 46

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 47

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 48

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 49

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 50

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 51

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 52

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 53

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 54

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 55

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 56

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 57

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 58

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 59

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 60

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 61

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 62

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 63

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 64

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 65

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10D Image 66

Exercise 10E page: 409

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 1

1. x2 + y2 = 4

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 2

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 3

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 4

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 5

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 6

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 7

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 8

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 9

5. xy = c2

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 10

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 11

6. x2 + y2 – 3xy = 1

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 12

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 13

7. xy2 – x2 y – 5 = 0

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 14

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 15

8. (x2 + y2)2 = xy

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 16

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 17

9. x2 + y 2 = log (xy)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 18

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 19

10. xn + yn = an

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 20

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 21

11. x sin 2y = y cos 2x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 22

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 23

12. sin2x + 2cos y + xy = 0

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 24

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10E Image 25

Exercise 10F page: 425

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 1

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 2

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 3

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 4

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 5

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 6

3. y = (log x)x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 7

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 8

4. y = x sinx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 9

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 10

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 11

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 12

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 13

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 14

7. y = (sinx) cosx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 15

8. y = (log x) sinx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 16

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 17

9. y = (cos x) logx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 18

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 19

10. y = (tan x) sinx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 20

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 21

11. y = (cos x) cosx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 22

12. y = (tan x) cotx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 23

13. y = x sin2x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 24

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 25

14. y = (sin-1 x)x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 26

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 27

15. y = sin (xx)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 28

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 29

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 30

16. y = (3x + 5) (2x – 3)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 31

17. y = (x + 1)3 (x + 2)4 (x + 3)5

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 32

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 33

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 34

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 35

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 36

19. y = (2x – 3)3 (3 + 2x)5

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 37

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 38

20. y = cos x cos 2x cos 3x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 39

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 40

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 41

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 42

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 43

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 44

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 45

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 46

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 47

Solution:

Logy = log [ x1/2 (3x + 5

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 48

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 49

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 50

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 51

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 52

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 53

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 54

26. y = sin 2x sin 3x sin 4x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 55

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 56

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 57

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 58

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 59

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 60

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 61

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 62

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 63

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 64

30. y = (1 + x) (1 + x2) (1 + x4) (1 + x6)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 65

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 66

31. y = xx – 2sinx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 67

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 68

32. y = (log x)x + x logx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 69

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 70

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 71

33. y = x sinx + (sin x) cosx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 72

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10F Image 73

Exercise 10G page: 435

1. If RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 1, prove that RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 2

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 3

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 4

2. If  RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 5, prove that RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 6

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 7

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 8

3. If RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 9, prove that RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 10.

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 11

4. If RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 12, prove that RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 13.

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10G Image 14

Exercise 10H page: 438

1. Differentiate x6 with respect to (1/ √x).

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 1

2. Differentiate log x with respect to cot x.

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 2

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 3

3. Differentiate e sinx with respect to cos x.

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 4

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 5

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 6

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 7

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 8

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 9

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 10

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 11

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 12

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10H Image 13

Exercise 10I page: 442

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 1

1. x = at2, y = 2at

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 2

2. x = a cos θ, y = b sin θ

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 3

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 4

3. x = a cos2 θ, y = b sin2 θ

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 5

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 6

4. x = a cos3 θ, y = a sin3 θ

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 7

5. x = a (1 – cos θ), y = a (θ + sin θ)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 8

6. x = a log t, y = b sin t

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 9

7. x = (log t + cos t), y = (et + sin t)

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 10

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 11

8. x = cos θ + cos 2θ, y = sin θ + sin 2θ

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 12

9. x = √sin 2θ, y = √cos 2θ

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 13

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 14

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 15

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 16

11. x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ).

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10I Image 17

Exercise 10J page: 449

1. Find the second derivative of:

(i) x11

(ii) 5x

(iii) tan x

(iv) cos -1 x

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 1

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 2

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 3

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 4

2. Find the second derivative of:

(i) x sin x

(ii) e 2x cos 3x

(iii) x3 logx

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 5

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 6

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 7

3. If y = x + tan x, show thatRS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 8.

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 9

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 10

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 11

Therefore, it is proved.

5. If y = 3 cos (log x) + 4 sin (log x), prove that x2y2 + xy1 + y = 0.

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 12

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 13

Therefore, it is proved.

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 14

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 15

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 16

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 17

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 18

Therefore, it is proved.

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 19

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 20

Therefore, it is proved.

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 21

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 22

Therefore, it is proved.

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 23

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 24

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 25

11. If y = a cos (log x) + b sin (log x), prove that x2 y2 + xy1 + y = 0

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 26

Therefore, it is proved.

12. Find the second derivative of e3x sin 4x.

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 27

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 28

13. Find the second derivative of sin 3x cos 5x.

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 29

Therefore, it is proved.

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 30

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 31

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 32

Therefore, it is proved.

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 33

Solution:

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 34

RS Aggarwal Solutions for Class 12 Chapter 10 Ex 10J Image 35

Therefore, it is proved.


Leave a Comment

Your email address will not be published. Required fields are marked *