# RS Aggarwal Solutions for Class 12 Maths 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 BYJUâ€™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 Maths Chapter 10: Differentiation Download PDF

### 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 Maths 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

2. cos 5x

Solution:

3. tan 3x

Solution:

4. cos x3

Solution:

5. cot2 x

Solution:

6. tan3 x

Solution:

7. cot âˆšx

Solution:

8. âˆštan x

Solution:

9. (5 + 7x) 6

Solution:

10. (3 â€“ 4x) 5

Solution:

11. (2x2 â€“ 3x + 4) 5

Solution:

12. (ax2 + bx + c) 6

Solution:

13. 1/ (x2 â€“ 3x + 5) 3

Solution:

Solution:

Solution:

16. cos2 x3

Solution:

17. sec3 (x2 + 1)

Solution:

Exercise 10B PAGE: 379

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

1. (i) e4x

(ii) e-5x

(iii) ex3

Solution:

Solution:

Solution:

4. (i) tan (logx)

(ii) log sec x

(iii) log sin x/2

Solution:

5. (i) log3x

(ii) 2-x

(iii) 3x+2

Solution:

Solution:

Solution:

Solution:

9. e 2x sin3x

Solution:

10. e 3x cos2x

Solution:

11. e-5x cot4x

Solution:

Exercise 10C PAGE: 388

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

1. cos-1 2x

Solution:

2. tan-1 x2

Solution:

3. sec-1 âˆšÂ x

Solution:

4. sin-1 x/a

Solution:

5. tan-1 (log x)

Solution:

6. cot-1 (ex)

Solution:

7. log (tan-1 x)

Solution:

8. cot-1 x3

Solution:

9. sin-1 (cos x)

Solution:

We know that

y = sin-1 (cos x)

It can be written as

y = sin-1 sin [Ï€/2 â€“ x]

So we get

y = Ï€/2 â€“ x

By differentiating both sides w.r.t. x

10. (1 + x2) tan-1 x

Solution:

Exercise 10D page: 402

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

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

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

Solution:

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

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

18. sin -1 (3x â€“ 4x3)

Solution:

19. sin -1 (1 â€“ 2x2)

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

Exercise 10E page: 409

1. x2 + y2 = 4

Solution:

Solution:

Solution:

Solution:

5. xy = c2

Solution:

6. x2 + y2 â€“ 3xy = 1

Solution:

7. xy2 â€“ x2 y â€“ 5 = 0

Solution:

8. (x2 + y2)2 = xy

Solution:

9. x2 + y 2 = log (xy)

Solution:

10. xn + yn = an

Solution:

11. x sin 2y = y cos 2x

Solution:

12. sin2x + 2cos y + xy = 0

Solution:

Exercise 10F page: 425

Solution:

Solution:

3. y = (log x)x

Solution:

4. y = x sinx

Solution:

Solution:

Solution:

7. y = (sinx) cosx

Solution:

8. y = (log x) sinx

Solution:

9. y = (cos x) logx

Solution:

10. y = (tan x) sinx

Solution:

11. y = (cos x) cosx

Solution:

12. y = (tan x) cotx

Solution:

13. y = x sin2x

Solution:

14. y = (sin-1 x)x

Solution:

15. y = sin (xx)

Solution:

16. y = (3x + 5) (2x â€“ 3)

Solution:

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

Solution:

Solution:

19. y = (2x â€“ 3)3 (3 + 2x)5

Solution:

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

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:

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

Solution:

Solution:

Solution:

Solution:

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

Solution:

31. y = xx â€“ 2sinx

Solution:

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

Solution:

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

Solution:

Exercise 10G page: 435

1. If , prove that

Solution:

2. If Â , prove that

Solution:

3. If , prove that .

Solution:

4. If , prove that .

Solution:

Exercise 10H page: 438

1. Differentiate x6 with respect to (1/ âˆšx).

Solution:

2. Differentiate log x with respect to cot x.

Solution:

3. Differentiate e sinx with respect to cos x.

Solution:

Solution:

Solution:

Exercise 10I page: 442

1. x = at2, y = 2at

Solution:

2. x = a cos Î¸, y = b sin Î¸

Solution:

3. x = a cos2 Î¸, y = b sin2 Î¸

Solution:

4. x = a cos3 Î¸, y = a sin3 Î¸

Solution:

5. x = a (1 â€“ cos Î¸), y = a (Î¸ + sin Î¸)

Solution:

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

Solution:

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

Solution:

8. x = cos Î¸ + cos 2Î¸, y = sin Î¸ + sin 2Î¸

Solution:

9. x = âˆšsin 2Î¸, y = âˆšcos 2Î¸

Solution:

Solution:

11. x = a (cos Î¸ + Î¸ sin Î¸), y = a (sin Î¸ â€“ Î¸ cos Î¸).

Solution:

Exercise 10J page: 449

1. Find the second derivative of:

(i) x11

(ii) 5x

(iii) tan x

(iv) cos -1 x

Solution:

2. Find the second derivative of:

(i) x sin x

(ii) e 2x cos 3x

(iii) x3 logx

Solution:

3. If y = x + tan x, show that.

Solution:

Solution:

Therefore, it is proved.

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

Solution:

Therefore, it is proved.

Solution:

Solution:

Therefore, it is proved.

Solution:

Therefore, it is proved.

Solution:

Therefore, it is proved.

Solution:

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

Solution:

Therefore, it is proved.

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

Solution:

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

Solution:

Therefore, it is proved.

Solution:

Therefore, it is proved.

Solution:

Therefore, it is proved.