Class 12 Maths NCERT Solutions of exercise 5.2 Chapter- Continuity and Differentiability - Future Study Point

Class 12 Maths NCERT Solutions of exercise 5.2 Chapter- Continuity and Differentiability

class 12 maths-contenuety and differentiability

 Class 12 Maths NCERT Solutions of exercise 5.2 Chapter- Continuity and Differentiability

 Class 12 maths NCERT  solution of exercise 5.2 -Continuity and differentiability will help all students of 12 class who are studying mathematics. From NCERT  Solutions of exercise 5.2 -Continuity and differentiability class 12 maths textbook you can understand the differentiation of the complex functions like trigonometric functions, rational functions etc.and the derivation of the greatest integer function. On these NCERT solutions of exercise 5.2- Continuity and differentiability, you will get complete knowledge of the chain rule of differentiation. The NCERT Solutions of exercise 5.2 is very easy to understand for the student so students can get the advantage of this by studying exercise 5.2 – Continuity and differentiability.

class 12 maths-contenuety and differentiability


Exercise 5.1-Continuity and Differentiability

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 Class 12 Maths NCERT Solutions of exercise 5.2 Chapter- Continuity and Differentiability

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Exercise 5.2

Differentiate the functions with respect to x in Questions 1 to 8.

Q1.sin( x² + 5)

Let  y = sin( x² + 5)  and t = x² + 5

y = sin t

t = x² + 5


= 2x.cos(x² + 5)

Q2. cos(sin x)

Let y = cos(sinx) and t = sin x

y = cos t

t = sin x

Substituting t = sinx

Q3. sin(ax + b)

Let y = sin(ax + b) and t = ax + b

y = sint

t = ax + b

Substituting t = ax + b


Ans. Let y = sec(tan√x) and t = tan √x

y = sec t


t = tan √x

According to the chain rule

Now, we have


Substituting the value of t


Now evaluating, by chain rule

We have


Differentiating the function with respect to x both sides

Let t= x5


t= x5

Similarly, we can evaluate



Q8. cot (√x)

Let y =cot (√x)

Let √x = t

Substituting value of t

Q9. Prove that the function f  given by

, x ∈ R is not differentiable at x = 1



It is known that a function f is differentiable at a point x ∈ R in its domain if both

LHS limit = RHS limit

LHS limit

x = 1

LHS limit



Therefore f(x) is not differentiable at  x= 1

Q10.Prove that the greatest integer function defined by is not differentiable at x= 1 and  x= 2.

Ans. Given:





The greatest value of the function at  1-h   im the domain 0 < x < 3  is = 0

= ∞



The greatest value at  1+ h of the function when h tends to 0 is =1


Therefore the function is not differentiable at x =1

Let’s check at x = 2


The value of greatest iteger fuctio [2-h ] = 1

= ∞


Simce x = 2

The value of greatest fuctio at [ 2 + h] = 2

Therefore f(x) is ot differetiale at x = 2

Himt:  1) If there exist the greatest integer fuctiom [x]   the value of  [1.099] = 1 ,[0.99] = 0 , [2.099] =2, [1.999]=1

[1 +h] = 1 and  [ 1- h] = 0, [2 + h] = 2 and [2-h] where h →0 .

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NCERT Solutions of Science and Maths for Class 9,10,11 and 12

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Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
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Chapter 4- Carbon and its CompoundsChapter 12- Electricity
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NCERT Solutions for class 11 maths

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Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
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NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
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