R S Aggarwal Solutions for Class 11 Maths Chapter 28 Differentiation Exercise 28B

Exercise 28B of Chapter 28 – Differentiation, problems are based on “derivative from the first principle”. All questions are solved by subject experts at BYJU’S with step-by-step explanation which helps students in understanding the concepts easily and quickly. Download R S Aggarwal Class 11 Chapter 28 exercise 28B solutions from the link given below.

Class 11 Maths Chapter 28 Differentiation Exercise 28B is based on the topic: Derivative from the first principle.

First Principle Statement

Download PDF of R S Aggarwal Solutions for Class 11 Maths Chapter 28 Differentiation Exercise 28B

 

rs aggarwal solution class 11 maths chapter 28 ex b
rs aggarwal solution class 11 maths chapter 28 ex b
rs aggarwal solution class 11 maths chapter 28 ex b
rs aggarwal solution class 11 maths chapter 28 ex b
rs aggarwal solution class 11 maths chapter 28 ex b
rs aggarwal solution class 11 maths chapter 28 ex b
rs aggarwal solution class 11 maths chapter 28 ex b
rs aggarwal solution class 11 maths chapter 28 ex b
rs aggarwal solution class 11 maths chapter 28 ex b

 

Access Answers to Maths R S Aggarwal Class 11 Chapter 28 Differentiation Exercise 28B Page number 875

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

R S Aggarwal Class 11 chapter 28

……………..(1)

Question 1: Derivate (ax + b)

Solution:

Let f(x) = ax + b ….(i)

Find f’(x) using first principle.

Now,

f(x + h) = a(x + h) + b = ax + ah + b …..(ii)

Subtract (i) form (ii)

f(x + h) – f(x) = ax + ah + b – ax – b = ah

From (1), we get

f’(x) = lim(h->0) {ah/h} = a

Question 2: Derivate

R S Aggarwal Class 11 chapter 28 Ex 28B question 2

Solution:

R S Aggarwal Class 11 chapter 28 Ex 28B question 2 solution

Question 3: Derivate 3x2 + 2x – 5

Solution:

Let f(x) = 3x2 + 2x – 5….(i)

Find f’(x) using first principle.

Now,

f(x + h) = 3(x+h)2 + 2(x+h) – 5

= 3x2 + 3h2 + 6xh + 2x + 2h – 5 …..(ii)

Subtract (i) form (ii)

f(x + h) – f(x) = 3x2 + 3h2 + 6xh + 2x + 2h – 5 – 3x2 – 2x + 5

= 3h2 + 6xh + 2h

From (1), we get

f’(x) = lim(h->0) {(3h2 + 6xh + 2h)/h} = 6x + 2

Question 4: Derivate x3 – 2x2 + x + 3

Solution:

Let f(x) = x3 – 2x2 + x + 3 …….(i)

Find f’(x) using first principle.

Now,

f(x + h) = (x+h)3 – 2(x+h)2 + (x + h) + 3 …..(ii)

Subtract (i) form (ii)

f(x + h) – f(x) = (x+h)3 – 2(x+h)2 + (x + h) + 3 – x3 + 2x2 – x – 3

= [(x+h)3 – x3] – 2[(x+h)2 – x2] + [x + h – x] [Using the identities:

(a + b) 3 = a3 + b3 + 3ab2 + 3a2b

(a + b) 2 = a2 + b2 + 2ab ]

= h3 + 3xh2 + 3x2h – 2[h2 + 2xh] + h

From (1), we get

R S Aggarwal Class 11 chapter 28 Ex 28B question 4 solution

Question 5: Derivate x8

Solution:

Let f(x) = x8

Find f’(x) using first principle.

Now,

f(x + h) = (x+h)8

From (1), we get

R S Aggarwal Class 11 chapter 28 Ex 28B question 5 solution

Question 6: Derivate 1/x3

Solution:

Let f(x) = 1/x3

Find f’(x) using first principle.

Now,

f(x + h) = 1/(x+h)3

From (1), we get

R S Aggarwal Class 11 chapter 28 Ex 28B question 6 solution

Question 7: Derivate 1/x5

Solution:

Let f(x) = 1/x5

Find f’(x) using first principle.

Now,

f(x + h) = 1/(x+h)5

From (1), we get

R S Aggarwal Class 11 chapter 28 Ex 28B question 7 solution

Question 8: Derivate √(ax+b)

Solution:

Let f(x) = √(ax+b)

Find f’(x) using first principle.

Now,

f(x + h) = √(a(x+h) +b)

From (1), we get

R S Aggarwal Class 11 chapter 28 Ex 28B question 8 solution

Question 9: Derivate √(5x-4)

Solution:

Let f(x) = √(5x-4)

Find f’(x) using first principle.

Now,

f(x + h) = √(5(x+h) – 4)

From (1), we get

R S Aggarwal Class 11 chapter 28 Ex 28B question 9 solution

Question 10: Derivate 1/√(x+2)

Solution:

Let f(x) = 1/√(x+2)

Find f’(x) using first principle.

Now,

f(x + h) = 1/√((x+h) +2)

From (1), we get

R S Aggarwal Class 11 chapter 28 Ex 28B question 10 solution

Question 11: Derivate 1/√(2x+3)

Solution:

Let f(x) = 1/√(2x+3)

Find f’(x) using first principle.

Now,

f(x + h) = 1/√(2(x+h) +3)

From (1), we get

R S Aggarwal Class 11 chapter 28 Ex 28B question 11 solution

Question 12: Derivate 1/√(6x-5)

Solution:

Let f(x) = 1/√(6x-5)

Find f’(x) using first principle.

Now,

f(x + h) = 1/√(6(x+h) – 5)

From (1), we get

R S Aggarwal Class 11 chapter 28 Ex 28B question 12 solution


Access other exercise solutions of Class 11 Maths Chapter 28 Differentiation

Exercise 28A Solutions

Exercise 28C Solutions

Exercise 28D Solutions

Exercise 28E Solutions

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