RS Aggarwal Solutions for Class 12 Chapter 10: Differentiation Exercise 10J

Second-order derivatives is the topic discussed under the Exercise 10J. Students who have doubts while solving the problems can refer to the PDF of solutions. The main aim is to improve logical thinking abilities and time management skills among students which are important from the exam point of view. Students can score good marks in the board exam by using RS Aggarwal Solutions Class 12 Maths Chapter 10 Differentiation Exercise 10J PDF as a vital study material during the exam preparation.

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

 

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Access other exercise solutions of 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

Access RS Aggarwal Solutions for Class 12 Chapter 10: Differentiation Exercise 10J

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.

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