JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > NCERT Solutions Exercise 5.4: Continuity & Differentiability
NCERT Solutions Exercise 5.4: Continuity & Differentiability
Q1: Differentiate the following w.r.t. x: 
Ans: Let y = 
By using the quotient rule, we obtain
Q2: Differentiate the following w.r.t. x: esin-1x
Ans: Let y = esin-1x
By using the chain rule, we obtain
Q3: Differentiate the following w.r.t. x: 
Ans: Let y = 
By using the chain rule, we obtain
Q4: Differentiate the following w.r.t. x: sin(tan-1e-x)
Ans: Let y = sin(tan-1e-x)
By using the chain rule, we obtain
Q5: Differentiate the following w.r.t. x: log(cosex)
Ans: Let y = log(cosex)
By using the chain rule, we obtain
Q6: Differentiate the following w.r.t. x:
Ans:
Q7: Differentiate the following w.r.t. x: 
Ans: Let
Q8: Differentiate the following w.r.t. x:
Ans: Let y = 
By using the chain rule, we obtain
Q9: Differentiate the following w.r.t. x:
Ans: Let y = 
By using the quotient rule, we obtain
Q10: Differentiate the following w.r.t. x: 
, x>0
Ans: Let y = 
By using the chain rule, we obtain
The document NCERT Solutions Exercise 5.4: Continuity & Differentiability is a part of the JEE Course Mathematics (Maths) Class 12.
All you need of JEE at this link: JEE
FAQs on NCERT Solutions Exercise 5.4: Continuity & Differentiability
| 1. What is the difference between continuity and differentiability in calculus? |  |
Ans. Continuity refers to the smoothness of a function where there are no breaks, jumps, or holes. Differentiability, on the other hand, refers to the existence of a derivative at a point, indicating the rate at which the function changes at that point.
| 2. How do you determine if a function is continuous at a point? | |
Ans. To determine if a function is continuous at a point, check if the function is defined at that point, the limit of the function exists at that point, and the value of the function equals the limit at that point.
| 3. Can a function be continuous but not differentiable? | |
Ans. Yes, a function can be continuous but not differentiable at a point if there is a sharp corner, cusp, or vertical tangent at that point. In such cases, the function is continuous but the derivative does not exist.
| 4. What is the significance of continuity and differentiability in real-world applications? | |
Ans. Continuity and differentiability are crucial in real-world applications such as physics, engineering, and economics. They help in analyzing rates of change, determining maximum and minimum values, and understanding the behavior of functions in various scenarios.
| 5. How can we determine if a function is differentiable at a point using limits? | |
Ans. To determine if a function is differentiable at a point using limits, calculate the limit of the difference quotient as it approaches zero. If the limit exists, the function is differentiable at that point.
About this Document
1.9K Views
4.60/5 Rating
Apr 21, 2026 Last updated
Document Description: NCERT Solutions Exercise 5.4: Continuity & Differentiability for JEE 2026 is part of Mathematics (Maths) Class 12 preparation. The notes and questions for NCERT Solutions Exercise 5.4: Continuity & Differentiability have been prepared according to the JEE exam syllabus. Information about NCERT Solutions Exercise 5.4: Continuity & Differentiability covers topics like and NCERT Solutions Exercise 5.4: Continuity & Differentiability Example, for JEE 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for NCERT Solutions Exercise 5.4: Continuity & Differentiability.
Introduction of NCERT Solutions Exercise 5.4: Continuity & Differentiability in English is available as part of our Mathematics (Maths) Class 12 for JEE & NCERT Solutions Exercise 5.4: Continuity & Differentiability in Hindi for Mathematics (Maths) Class 12 course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: NCERT Solutions Exercise 5.4: Continuity & Differentiability
Description
NCERT Solutions Exercise 5.4: Continuity & Differentiability of Maths Class 12 provides all the questions of NCERT textbook with detailed solutions. Download free PDF from EduRev.
Information about NCERT Solutions Exercise 5.4: Continuity & Differentiability
In this doc you can find the meaning of NCERT Solutions Exercise 5.4: Continuity & Differentiability defined & explained in the simplest way possible. Besides explaining types of NCERT Solutions Exercise 5.4: Continuity & Differentiability theory, EduRev gives you an ample number of questions to practice NCERT Solutions Exercise 5.4: Continuity & Differentiability tests, examples and also practice JEE tests
Related Searches
Free, Sample Paper, Objective type Questions, Previous Year Questions with Solutions, Summary, Viva Questions, ppt, NCERT Solutions Exercise 5.4: Continuity & Differentiability, Important questions, Semester Notes, past year papers, mock tests for examination, study material, MCQs, pdf , Extra Questions, video lectures, shortcuts and tricks, NCERT Solutions Exercise 5.4: Continuity & Differentiability, Exam, NCERT Solutions Exercise 5.4: Continuity & Differentiability, practice quizzes;