RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 10. Differentiation

Subject: Maths - Class 12th

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Chapter Exercises

Exercise 10A
Exercise 10B
Exercise 10C
Exercise 10D
Exercise 10E
Exercise 10F
Exercise 10G
Exercise 10H
Exercise 10I
Exercise 10J

Exercise 10A

1

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

sin 4x
2

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

cos 5x
3

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

tan 3x
4

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

cos x3
5

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

cot2x
6

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

tan3x
7

Differentiate each of the following w.r.t. x:
8

Differentiate each of the following w.r.t. x:
9

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

(5 + 7x)6
10

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

(3 – 4x )5
11

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

(2x2 – 3x +4)5
12

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

(

13

Differentiate each of the following w.r.t. x:
14

Differentiate each of the following w.r.t. x:
15

Differentiate each of the following w.r.t. x:
16

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

cos2

17

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

sec3 (

18

Differentiate each of the following w.r.t. x:
19

Differentiate each of the following w.r.t. x:
20

Differentiate each of the following w.r.t. x:
21

Differentiate each of the following w.r.t. x:
22

Differentiate each of the following w.r.t. x:
23

Differentiate each of the following w.r.t. x:
24

Differentiate each of the following w.r.t. x:
25

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

cot3

26

Differentiate each of the following w.r.t. x:
27

Differentiate each of the following w.r.t. x:
28

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

sin 5

29

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

sin 2

30

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

cos 4

31

Find , when:

32

Find , when:

33

If

34

If

Exercise 10B

1

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

(i)


(ii)


(iii)


2

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

(i)


(ii)


(iii)


3

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

(i)


(ii)


(iii)


4

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

(i) tan (log x)


(ii) log (sec x)


(iii) log (sin (x/2))
5

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

(i)log3 x


(ii)


(iii)


6

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

(i)


(ii) log (sin (3x))


(iii)


7

Differentiate each of the following w.r.t. x:
8

Differentiate each of the following w.r.t. x:
9

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

e2x sin 3x
10

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

e3x cos 2x
11

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

e-5x cot 4x
12

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

ex log (sin 2x)
13

Differentiate each of the following w.r.t. x:
14

Differentiate each of the following w.r.t. x:
15

Differentiate each of the following w.r.t. x:
16

Differentiate each of the following w.r.t. x:
17

Differentiate each of the following w.r.t. x:
18

Differentiate each of the following w.r.t. x:
19

Differentiate each of the following w.r.t. x:
20

Differentiate each of the following w.r.t. x:
21

Differentiate each of the following w.r.t. x:
22

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

Exercise 10C

1

Differentiate each of the following w.r.t. x:
2

Differentiate each of the following w.r.t. x:
3

Differentiate each of the following w.r.t. x:
4

Differentiate each of the following w.r.t. x:
5

Differentiate each of the following w.r.t. x:
6

Differentiate each of the following w.r.t. x:
7

Differentiate each of the following w.r.t. x:
8

Differentiate each of the following w.r.t. x:
9

Differentiate each of the following w.r.t. x:
10

Differentiate each of the following w.r.t. x:
11

Differentiate each of the following w.r.t. x:
12

Differentiate each of the following w.r.t. x:
13

Differentiate each of the following w.r.t. x:
14

Differentiate each of the following w.r.t. x:
15

Differentiate each of the following w.r.t. x:
16

Differentiate each of the following w.r.t. x:
17

Differentiate each of the following w.r.t. x:
18

If prove that .
19

Prove that .

Exercise 10D

1

Differentiate each of the following w.r.t x:
2

Differentiate each of the following w.r.t x:
3

Differentiate each of the following w.r.t x:
4

Differentiate each of the following w.r.t x:
5

Differentiate each of the following w.r.t x:
6

Differentiate each of the following w.r.t x:
7

Differentiate each of the following w.r.t x:
8

Differentiate each of the following w.r.t x:
9

Differentiate each of the following w.r.t x:
10

Differentiate each of the following w.r.t x:
11

Differentiate each of the following w.r.t x:
12

Differentiate each of the following w.r.t x:
13

Differentiate each of the following w.r.t x:
14

Differentiate each of the following w.r.t x:
15

Differentiate each of the following w.r.t x:
16

Differentiate each of the following w.r.t x:
17

Differentiate each of the following w.r.t x:
18

Differentiate each of the following w.r.t x:
19

Differentiate each of the following w.r.t x:
20

Differentiate each of the following w.r.t x:
21

Differentiate each of the following w.r.t x:
22

Differentiate each of the following w.r.t x:
23

Differentiate each of the following w.r.t x:
24

Differentiate each of the following w.r.t x:
25

Differentiate each of the following w.r.t x:
26

Differentiate each of the following w.r.t x:
27

Differentiate each of the following w.r.t x:
28

Differentiate each of the following w.r.t x:
29

Differentiate each of the following w.r.t x:
30

Differentiate each of the following w.r.t x:
31

Differentiate each of the following w.r.t x:
32

Differentiate each of the following w.r.t x:
33

Differentiate each of the following w.r.t x:
34

Differentiate each of the following w.r.t x:
35

Differentiate each of the following w.r.t x:
36

Differentiate each of the following w.r.t x:
37

Differentiate each of the following w.r.t x:
38

Differentiate each of the following w.r.t x:
39

Differentiate each of the following w.r.t x:
40

Differentiate each of the following w.r.t x:
41

Differentiate each of the following w.r.t x:
42

Differentiate each of the following w.r.t x:
43

Differentiate each of the following w.r.t x:
44

Differentiate each of the following w.r.t x:
45

Differentiate each of the following w.r.t x:
46

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

If , prove that .
47

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

If , show that .
48

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

If , show that


49

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

If , show that .
50

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

If . Prove that .
51

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

Differentiate w. r. t. x

Exercise 10E

1

Find , when:

x2 + y2 = 4
2

Find , when:
3

Find , when:
4

Find , when:
5

Find , when:

xy = c2
6

Find , when:

x2 + y2 — 3xy = 1
7

Find , when:

xy2 — x2y — 5 = 0
8

Find , when:

(x2 + y2)2 = xy
9

Find , when:

x2 + y2 = log (xy)
10

Find , when:

xn + yn = an
11

Find , when:

x sin 2y = y cos 2x
12

Find , when:

sin2x + 2cos y + xy
13

Find , when:

y sec x + tan x + x2y = 0
14

Find , when:

cot (xy) + xy = y
15

Find , when:

y tan x — y2 cos x + 2x = 0
16

Find , when:

ex log y = sin—1 x + sin —1y
17

Find , when:

xy log (x + y) = 1
18

Find , when:

tan (x + y) + tan (x — y) = 1
19

Find , when:
20

Find , when:

If y = x sin y , prove that .


There is correction in question …. Prove that should be
instead of to get the required answer.
21

Find , when:

If xy = tan (xy), show that .
22

Find , when:

If y log x = (x — y), prove that .
23

Find , when:

If cos y = x cos (y + a), prove that .
24

Find , when:

If , prove that .

Exercise 10F

1

Find , when:
2

Find , when:
3

Find , when:
4

Find , when:
5

Find , when:
6

Find , when:
7

Find , when:
8

Find , when:
9

Find , when:
10

Find , when:
11

Find , when:
12

Find , when:
13

Find , when:
14

Find , when:
15

Find , when:
16

Find , when:
17

Find , when:
18

Find , when:
19

Find , when:
20

Find , when:
21

Find , when:
22

Find , when:
23

Find , when:
24

Find , when:
25

Find , when:
26

Find , when:
27

Find , when:
28

Find , when:
29

Find , when:
30

Find , when:
31

Find , when:
32

Find , when:
33

Find , when:
34

Find , when:
35

Find , when:
36

Find , when:
37

Find , when:
38

Find , when:
39

Find , when:
40

Find , when:
41

Find , when:
42

Find , when:
43

Find , when:
44

If , prove that .
45

If , prove that .
46

If , prove that .
47

If , show that

48

If , prove that

49

If , prove that .
50

If , prove that .
51

If , show that

52

If , show that

53

If , show that .
54

If , show that .
55

If , prove that ..
56

If , prove tha.
57

If ,

58

If , prove that .
59

If prove that .
60

If , find .
61

If , find .
62

If find .
63

If , find .
64

, find .
65

Find , when:

If , prove that .
66

If , prove that .

Exercise 10G

1

If , prove that
2

If , prove that

3

If , prove that

4

If, prove that
5

If prove that

6

If , show that

7

If , prove that

8

If prove that

Exercise 10H

1

Differentiate with respect to

2

Differentiate log with respect to

3

Differentiate with respect to .
4

Differentiate with respect to

5

Differentiate with respect to

6

Differentiate with respect to

7

Differentiate with respect to

8

Differentiate with respect to

9

Differentiate with respect to

10

Differentiate with respect to when

Exercise 10I

1

Find , when

2

Find , when

3

Find , when

4

Find , when

5

Find , when

6

Find , when

7

Find , when

8

Find , when

9

Find , when

10

Find , when

11

Find , when

12

Find , when

13

Find , when

14

Find , when

15

If

16

If

17

If

18

If

19

If

20

If

21

If

Exercise 10J

1

Find the second derivate of :

(i) x11 (ii) 5x


(iii) tan x (iv) cos-1x
2

Find the second derivative of:

(i) x sin x


(ii) e2x cos 3x


(iii) x3 log x
3

If

4

If

5

If

6

If y = e- cos x , show that = 2e-xsin x .
7

If

8

If

9

If

10

If

11

If

12

Find the second derivative of e3x sin 4x .
13

Find the second derivative of sin 3 x cos 5x.
14

If

15

If

16

If

17

If

18

If x = at2 and

19

If x = a(θ – sin θ ) and

20

If

21

If

22

If

23

If x = and

24

If x = cos t + log tan ,

25

If

26

If

27

If

28

If

29

If x = a(cos θ + θ sin θ ) and

30

If x = a cos θ + b sin θ and